Dopo che avremo mangiato, porterò alla nonna una fetta di torta ancora calda.

Because the sentence talks about two actions in the future, and one of them happens before the other:

• avremo mangiato = we will have eaten
• porterò = I will bring

Italian often uses the future perfect (futuro anteriore) after dopo che when it means after and the action is completed before another future action.

So:

• Dopo che avremo mangiato, porterò... = After we have eaten, I will bring...

This is very natural in Italian. English can also use after we have eaten, but often just says after we eat.

Avremo mangiato is the future perfect of mangiare.

It is made with:

• the future of avere: avrò, avrai, avrà, avremo, avrete, avranno
• • the past participle: mangiato

So:

• avremo = we will have
• mangiato = eaten

Together:

• avremo mangiato = we will have eaten

The subject is understood from the verb ending:

• avremo = we will have

So Italian does not need to say noi unless you want emphasis.

Because the speaker is describing a future action:

• porterò = I will bring

The whole sentence is about something that will happen later:

1. we will have eaten
2. I will bring a slice of cake to grandma

So the main verb naturally appears in the simple future:

• porterò

This is the future of portare.

Alla nonna means to grandma.

It is made of:

• a = to
• la = the
• a + la = alla

So:

• porterò alla nonna una fetta di torta = I will bring grandma a slice of cake or more literally = I will bring to grandma a slice of cake

Italian often uses a with the person receiving something.

Because Italian often uses the article with family terms in many contexts, especially when they are not being used as a direct form of address.

Here, la nonna means grandma / the grandmother, and with a it becomes alla nonna.

Compare:

• Parlo con la nonna = I’m speaking with grandma
• Porto un regalo alla nonna = I’m bringing a gift to grandma

But when directly addressing her, you usually do not use the article:

• Nonna, guarda! = Grandma, look!

Also, in some contexts with possessives, family words may behave differently:

• mia nonna = my grandmother
• not usually la mia nonna in the most basic neutral use

Because una fetta di torta means a slice of cake, not the whole cake.

Breakdown:

• una = a
• fetta = slice
• di = of
• torta = cake

So:

• una fetta di torta = a slice of cake

If you said porterò alla nonna una torta, that would mean I will bring grandma a cake — a whole cake.

It describes una fetta di torta.

So:

• una fetta di torta ancora calda = a slice of cake still warm

Here calda agrees with fetta, which is:

• singular
• feminine

That is why it is calda, not caldo.

Ancora here means still.

So the idea is that the cake slice is still warm at the time it is brought.

Actually, both fetta and torta are feminine singular, so calda would match either one grammatically. But in the structure of the sentence, ancora calda most naturally refers to the noun phrase being brought, especially fetta.

Main point:

• fetta = feminine singular
• torta = feminine singular
• so the adjective must be calda

If the noun were masculine, you would use caldo:

• un pezzo di pane ancora caldo = a piece of bread still warm

Both are possible.

Italian word order is more flexible than English. These are both natural:

• Porterò alla nonna una fetta di torta
• Porterò una fetta di torta alla nonna

The difference is mostly about focus or style, not basic meaning.

• alla nonna earlier can highlight who receives it
• una fetta di torta earlier can highlight what is being brought

So the original sentence is perfectly normal, but not the only possible order.

Yes, often you can.

• Dopo che avremo mangiato, porterò...
• Dopo aver mangiato, porterò...

Both can mean After eating / After we have eaten, I will bring...

But there is a small difference:

• dopo che avremo mangiato explicitly states a future completed action
• dopo aver mangiato is a more compact infinitive structure, like after eating or after having eaten

In everyday Italian, both are common, depending on style and context.

In a sentence clearly referring to the future, standard Italian commonly prefers the future perfect here:

• Dopo che avremo mangiato...

English often says:

• After we eat...

But Italian is usually more precise about the future sequence of events.

In informal speech, you may sometimes hear simpler structures, but for standard grammar and careful usage, dopo che + futuro anteriore is a very good choice when one future action happens before another.

Because Italian verb endings usually already show the subject.

• avremo tells you the subject is we
• porterò tells you the subject is I

So:

• (noi) avremo mangiato
• (io) porterò

The pronouns are optional unless you want contrast, emphasis, or clarity.

For example:

• Dopo che avremo mangiato, io porterò la torta e tu laverai i piatti. = After we’ve eaten, I’ll bring the cake and you’ll wash the dishes.

Here io and tu add contrast.

Usually, nonna is not capitalized in normal Italian spelling unless it begins a sentence.

So the standard form is:

• alla nonna

You might see Nonna in special contexts, such as:

• at the beginning of a sentence
• in letters or cards
• in a more name-like or affectionate style

But in ordinary running text, nonna is normally lowercase.