Learn Hardcore German: Die Pfanne ist zu klein, um alle Stücke gleichzeitig zu braten. - The pan is too small to fry all pieces at the same time.

Here it’s the pattern zu + adjective, um ... zu + infinitive, which means “too [adjective] to [do something].” So zu klein, um ... zu braten = “too small to fry ...”. It’s still an infinitive clause with um ... zu, but it expresses an impossibility due to the adjective, not an attainable purpose.

Why is there a comma before "um"?

German requires a comma before infinitive clauses introduced by um, ohne, (an)statt, außer, als. So you must write: Die Pfanne ist zu klein, um alle Stücke gleichzeitig zu braten.

Why is it zu braten and not zu bräten?

Because zu takes the bare infinitive. The verb’s infinitive is braten. The umlaut (ä) appears only in 2nd/3rd person singular present (e.g., du brätst, er/sie/es brät), not in the infinitive. Principal parts: braten – briet – gebraten.

What case is alle Stücke, and why is there no article?

alle Stücke is accusative plural, the direct object of braten inside the infinitive clause.
Stück is neuter (das Stück), plural die Stücke.
There’s no indefinite article in the plural, and alle already functions as a determiner, so alle Stücke (not alle die Stücke) is correct.

Can I drop um or say ... braten zu?

No. In this pattern you need um ... zu. Writing the clause without um is considered wrong or at best very colloquial.
zu must stand immediately before the infinitive: zu braten. braten zu is ungrammatical.

Does the um ... zu clause have the same subject as the main clause? The pan can’t fry things!

Normally um ... zu implies the same (understood) subject as the main clause. But with zu + Adj., um ... zu, German allows a generic implied subject (“one/you/we”). So it means: “The pan is too small for one to fry all the pieces at once.” If you want to avoid this mismatch, rephrase:

Die Pfanne ist so klein, dass man nicht alle Stücke gleichzeitig braten kann.
Die Pfanne ist zu klein, als dass man alle Stücke gleichzeitig braten könnte.

Could I use damit instead of um ... zu?

No. damit introduces a purpose clause with its own explicit subject and doesn’t fit the “too ... to ...” idea. Use:

Result: so ... dass — Die Pfanne ist so klein, dass man nicht alle Stücke gleichzeitig braten kann.
Negative result (more formal): zu ... als dass — see previous answer.

Where should gleichzeitig go?

Both are fine:

..., um alle Stücke gleichzeitig zu braten.
..., um gleichzeitig alle Stücke zu braten. Avoid placing it after the infinitive: ..., um alle Stücke zu braten gleichzeitig sounds wrong.

Is gleichzeitig the best word? What about auf einmal or zur selben Zeit?

gleichzeitig = simultaneously; neutral and idiomatic here.
auf einmal = in one go/in a single batch; also good here: ..., um alle Stücke auf einmal zu braten. (Note it can mean “suddenly” in other contexts.)
zur selben/gleichen Zeit is fine but wordier: ..., um alle Stücke zur selben Zeit zu braten.
zeitgleich is common for scheduled events; for cooking, gleichzeitig or auf einmal sounds more natural.

What’s the difference between zu klein and nicht groß genug?

They’re near-equivalents:

zu klein, um ... zu = “too small to ...”
nicht groß genug, um ... zu = “not big enough to ...” Example: Die Pfanne ist nicht groß genug, um alle Stücke gleichzeitig zu braten.

Why die Pfanne, and which case is it?

Pfanne is feminine, so nominative singular is die Pfanne. It’s the subject of ist (a linking verb), so nominative is required: Die Pfanne ist .... With an indefinite article: Eine Pfanne ist ....

What exactly does braten mean here? How is it different from backen or kochen?

braten = fry/roast in fat or dry heat (pan or oven). Transitive: etwas braten (“fry something”). Intransitive: etwas brät (“something is frying”).
backen = bake (bread, cakes; also “baked potatoes”).
kochen = cook/boil in liquid. A related verb: anbraten = sear/brown briefly.

Can I put the um ... zu clause first?

Yes: Um alle Stücke gleichzeitig zu braten, ist die Pfanne zu klein. It’s grammatical; many speakers keep it after the main clause unless they want to foreground that condition.

Is alle die Stücke acceptable?

Generally no. Use alle Stücke. Combine alle only with another determiner when specific: alle diese Stücke, alle meine Stücke, alle drei Stücke. alle die Stücke is clumsy or dialectal.

Can I use a noun phrase with zum Braten instead of the um ... zu clause?

Yes, but it’s more formal: Die Pfanne ist zu klein zum gleichzeitigen Braten aller Stücke. Here zum = zu dem, Braten is a noun, and aller Stücke is genitive.

Any pronunciation tips for Pfanne and Stücke?

Pfanne: initial pf is a single cluster; say both sounds quickly: [ˈpfanə].
Stücke: initial St is [ʃt] (“sht”); ü is like French “u”: [ˈʃtʏkə].