Learn Hardcore Dutch: Mijn tante kookt soep en is heel aardig.

In Dutch, mass/uncountable nouns used in a general sense usually take no article. kookt soep = “cooks soup (in general).”
If you mean a specific soup, use the definite article: kookt de soep.
You can use an indefinite form when you specify a type or portion: kookt een tomatensoep, neemt een soepje, kookt een pan soep. In everyday Dutch in the Netherlands, plain een soep is less common unless a kind is specified; in Belgium (Flemish) een soep is more common in the “a soup” sense.

Can I leave out the subject in the second clause like this, or should it be … en zij is heel aardig?

Both are correct. In coordinated main clauses, Dutch often omits a repeated subject:

Natural: Mijn tante kookt soep en is heel aardig.
Also fine: Mijn tante kookt soep en zij (ze) is heel aardig. Only omit the subject if it’s the same as in the first clause. If the subject changes, you must state it: Mijn tante kookt soep en mijn oom is heel aardig.

Does starting the second clause with is break the Dutch “verb-second” (V2) rule?

No. With coordinated clauses, when the subject is omitted because it’s the same as in clause 1, the finite verb can appear first in the second clause, and this is entirely natural. If you include the subject, V2 shows clearly: … en zij is heel aardig. In a subordinate clause, the verb goes to the end: … dat mijn tante soep kookt en heel aardig is.

Why is it aardig and not aardige after is?

After a linking verb like is, adjectives are predicative and stay in their base form: … is (heel) aardig. The -e ending appears mainly with attributive adjectives before a noun:

Predicative: Mijn tante is aardig.
Attributive: Mijn aardige tante… (because tante is a common-gender “de”-word). A well-known exception: with an indefinite neuter noun, no -e is used attributively: een aardig kind.

What’s the difference between heel, erg, zeer, and hartstikke?

heel = very; neutral and common: heel aardig.
erg = very; also common. Can combine: heel erg aardig (stronger).
zeer = very; more formal/literary: zeer aardig.
hartstikke = very; informal/colloquial: hartstikke aardig. All precede the adjective. Don’t say aardig heel.

Is koken the best verb with soep, or can I say maken?

Both are possible:

Idiomatic and very common: soep koken (“to cook/make soup” on the stove).
Also fine: soep maken (“to make soup”). Use the cooking verb that fits the dish: water koken (boil water), eieren koken (boil eggs), taart bakken (bake a cake), groente stomen (steam vegetables).

Why does the verb have -t in kookt?

Because the subject (mijn tante) is third-person singular. Present tense:

ik kook
jij/je kookt (but after inversion: kook jij?)
hij/zij/het kookt
wij/jullie/zij koken So here: Mijn tante kookt…. The second verb is is the irregular third-person singular of zijn.

Does Dutch present tense mean “right now” or “in general”?

Both, depending on context.

Habitual/general: Mijn tante kookt vaak soep.
Right now is often made explicit: Mijn tante kookt nu soep, or with a progressive construction: Mijn tante is soep aan het koken / Mijn tante is bezig soep te koken / Mijn tante staat te koken (she’s literally standing and cooking).

Should there be a comma before en?

Normally, no. Dutch does not require a comma before en in a simple coordination:

Mijn tante kookt soep en is heel aardig. You may add a comma only for readability in very long or complex sentences.

Why is it mijn tante without an article?

Possessive determiners like mijn, jouw, zijn, haar replace the article:

de tante → mijn tante (never de mijn tante). Note: tante is a common-gender “de”-word; if you use an adjective attributively, it takes -e: mijn aardige tante.

If I refer back to tante, do I use zij or ze?

Use the feminine pronoun: zij (stressed) or ze (unstressed).

Neutral: Ze kookt soep.
Contrast/emphasis: Zij kookt soep, niet hij. Use haar for “her” (possessive): haar soeprecept. For people, don’t use het even though some nouns are neuter; pronouns follow natural gender for people.

How do I pronounce the words in this sentence?

Approximate guide (Netherlands Dutch):

mijn: like English “mine” but shorter and tenser on the vowel; written ij is one sound [ɛi].
tante: TAHN-tuh; short a as in “father” but shorter; final -e is a schwa.
kookt: KOOKT with a long oo [oː]; pronounce the final -t and the -kt cluster.
soep: like English “soup,” but oe is [u] as in “food.”
en: like “en”; often reduced to a quick [ən].
is: like English “is,” with a short i [ɪ].
heel: HAYL with a long vowel [heːl].
aardig: AAR-dikh; long aa [aː], and the final g is a guttural fricative [x/ɣ] (in Flanders often softer).