Learn Hardcore Polish: Menu jest krótkie, ale lubimy zupę dnia. - The menu is short, but we like the soup of the day.

Because menu is treated as a neuter singular noun in Polish (it’s an indeclinable loanword). Adjectives describing neuter singular nouns in the nominative end in -e, hence krótkie.

Feminine example: Karta dań jest krótka.
Masculine example: Jadłospis jest krótki.
Neuter example: Menu jest krótkie.

Does menu decline in cases or change in the plural?

Menu is indeclinable: it stays menu in every case. With prepositions you still use menu, e.g., w menu (in the menu).

Singular: To menu jest krótkie.
Plural exists but the form is the same: Te menu są krótkie. (Adjectives/pronouns show the number.)

Why is it zupę and not zupa?

Because lubić takes a direct object in the accusative case. The noun zupa (feminine) changes to zupę in the accusative singular.

Nominative (dictionary form): zupa
Accusative: zupę

What is dnia doing there? Why not dzień?

Dnia is the genitive singular of dzień (day). Polish uses the genitive to express “of,” so zupa dnia literally means “soup of the day.”

Nominative: dzień
Genitive: dnia

Why zupę dnia here, but sometimes I see zupa dnia?

The base phrase is zupa dnia (soup of the day) in the nominative. In your sentence, the whole phrase is the direct object of lubimy, so the head noun zupa changes to the accusative (zupę), while dnia stays in the genitive:

Subject position: Zupa dnia jest pyszna.
Object position: Lubimy zupę dnia.

Could I say zupa dzienna or dzisiejsza zupa instead?

Zupa dnia is the standard, idiomatic menu phrase “soup of the day.”
Dzisiejsza zupa means “today’s soup” and is fine if you specifically mean today.
Zupa dzienna is not idiomatic for menus and sounds odd.
Very formal/old-fashioned: zupa dnia dzisiejszego.

Do I need to include the pronoun My (we)?

No. Polish usually drops subject pronouns because the verb ending shows the person/number. Lubimy already means “we like.” You can add My for emphasis or contrast: My lubimy zupę dnia.

Is lubić the right verb for liking food? What about smakować or podobać się?

Lubić + accusative expresses a general, stable preference: Lubię zupy.
Smakować + dative means “to taste good to someone” (judgment about taste at some moment): Zupa dnia nam smakuje.
Podobać się is for things that please you aesthetically; it’s not used for the taste of food. Prefer smakować for that.

How do you conjugate lubić in the present?

ja lubię
ty lubisz
on/ona/ono lubi
my lubimy
wy lubicie
oni/one lubią

Pronouns are usually omitted unless emphasized.

What happens under negation?

With negation, Polish typically changes a direct object from accusative to genitive. So:

Affirmative: Lubimy zupę dnia.
Negative: Nie lubimy zupy dnia.

Do I have to use jest? Can I say Menu krótkie?

In a normal declarative sentence, include jest: Menu jest krótkie.
Dropping jest is possible in headlines or very telegraphic styles. Another common structure is with to: To krótkie menu.

Why not instrumental after jest (e.g., krótkim)?

After być (jest), adjectives stay in the nominative (krótkie). The instrumental is commonly used with nouns after być to express profession/role: On jest lekarzem. But with adjectives, use nominative: Menu jest krótkie.

Is the comma before ale required?

Yes. In Polish, you always put a comma before ale when it links two clauses: …, ale …

Can I change the word order?

Yes. Polish allows flexibility for emphasis:

Lubimy zupę dnia, ale menu jest krótkie. (Starts with the positive.)
Zupę dnia lubimy, ale menu jest krótkie. (Emphasizes the soup.) Meaning stays the same; word order affects what you highlight.

Any pronunciation tips for tricky parts?

menu: stress the penultimate syllable: ME-nu; pronounced roughly meh-NOO.
krótkie: ó sounds like English “oo” (u): KROOT-kyeh.
lubimy: lu-BEE-mih (stress on BI).
zupę: ZOO-peh, with final ę as a nasalized “e”; in casual speech it can sound close to plain “e.”
dnia: sounds like “dnya” with a soft n: dnya. Polish stress is generally on the penultimate syllable of each word (where applicable).

Do I need an article like the or a anywhere?

No. Polish has no articles. Context handles definiteness. Zupę dnia corresponds to English “the soup of the day” without needing an article.

Are there synonyms for menu, and do they change the adjective?

Yes:

karta dań (feminine): Karta dań jest krótka.
jadłospis (masculine): Jadłospis jest krótki.
menu (neuter): Menu jest krótkie.

What nuance does krótkie convey about a menu?

Krótkie here means “brief/limited in choices,” not physically short. Near-synonyms for menus: skromne (modest), ograniczone (limited), niewielkie (small in scope).