imouto wa ninjin to tamanegi o itamenagara, ashita mo kono ryouri o tabetai to itte ita.

は marks 妹 as the topic of the sentence: as for my younger sister...

It does not just mark the grammatical subject; it frames what the sentence is about. In English, we often just say My younger sister..., but in Japanese, は is very common when introducing the person or thing the sentence will describe.

So here, the sentence is basically: As for my younger sister, while stir-frying carrots and onions, she was saying...

と connects the two nouns and means and.

So:

• にんじん と 玉ねぎ = carrots and onions

Then を marks the whole combined noun phrase as the object of 炒める (to fry / stir-fry).

So:

• にんじんと玉ねぎを炒める = to stir-fry carrots and onions

Japanese often puts one particle after the entire list rather than repeating it after each noun.

ながら means while doing...

It attaches to the verb stem:

• 炒める → 炒め
• 炒めながら = while stir-frying

So this shows that one action happens at the same time as another:

• stir-frying carrots and onions
• saying that she wants to eat this dish tomorrow too

A very important point: with ながら, the subject is normally the same for both actions. So the person stir-frying is also the person speaking: the younger sister.

Usually it means the actions overlap, with one serving as the background action.

Here:

• background action: stir-frying
• main action: saying

So it feels like: While she was stir-frying carrots and onions, she was saying...

It does not have to mean perfect split-second simultaneity; it just means the actions are occurring together in that scene.

明日 means tomorrow, and も means also / too.

So 明日も means:

• tomorrow too
• also tomorrow
• tomorrow as well

The nuance is that she wants to eat this dish tomorrow in addition to some other time, usually today or already now.

So the idea is something like: I want to eat this dish again tomorrow too.

The particle と marks the content of speech or thought before verbs like:

• 言う = to say
• 思う = to think

So:

• この料理を食べたい = (I) want to eat this dish
• この料理を食べたいと言っていた = was saying that she wanted to eat this dish

You can think of と here as marking a quotation, either direct or indirect.

That is a very common question.

It is true that 〜たい normally expresses the speaker’s own desire, so in plain narration you usually do not say:

• 妹はこの料理を食べたい。 to mean My younger sister wants to eat this dish.

Instead, you would often say:

• 妹はこの料理を食べたがっている。

But in this sentence, the desire is inside a quotation:

• この料理を食べたいと言っていた

That is perfectly natural, because you are reporting her own words. She said I want to eat this dish, so 食べたい is exactly right inside the quoted content.

言っていた is the past form of 言っている, and here it often gives the nuance of:

• was saying
• had said
• was saying repeatedly / in that situation
• said (as remembered/reported from that time)

Compared with 言った, 言っていた can sound more like recalling what someone was saying in an ongoing scene.

So in this sentence, it fits well because we are picturing her in the middle of cooking and saying this.

Very roughly:

• 言った = said
• 言っていた = was saying / had said

The subject is understood to be 妹.

Japanese often leaves subjects unstated when they are clear from context. Here, the quotation is:

• 明日もこの料理を食べたい

Since that is followed by と言っていた, we understand that this is what the younger sister was saying.

So the implied meaning is: My younger sister was saying, “I want to eat this dish tomorrow too.”

Inside the quoted part, from her point of view, the subject is basically I.

Japanese often puts background or accompanying actions before the main action.

So:

• にんじんと玉ねぎを炒めながら = background situation
• 明日もこの料理を食べたいと言っていた = main statement

This is very natural Japanese sentence flow: While doing X, she was doing Y.

English can do the same: While stir-frying carrots and onions, she was saying...

この料理 means this dish or this meal.

In context, it most naturally refers to the food she is currently making, or the dish being discussed in the situation. Japanese often relies on context for this kind of reference instead of spelling everything out.

So the sense is: this dish we’re making / this dish here

Most likely, yes.

Japanese family terms like 妹 often work like relational nouns and depend on context. In an ordinary sentence without extra explanation, 妹 usually means my younger sister or the younger sister relevant to the conversation.

Since no possessor is stated, English often translates it naturally as my younger sister if the speaker is talking about their own family member.

Yes, that is a reasonable natural translation.

A few possible English versions are:

• While stir-frying carrots and onions, my younger sister said she wants to eat this dish again tomorrow too.
• My younger sister was saying, while stir-frying carrots and onions, that she wants to eat this dish again tomorrow too.
• While stir-frying carrots and onions, my younger sister said she wanted to eat this dish again tomorrow too.

The best English tense depends on context. Japanese 言っていた can sometimes be rendered as was saying, said, or had said.