Learn Hardcore Turkish: Karantina başladığından beri yemek pişirmeye fırsatım oldu. - Since the quarantine began, I have had the opportunity to cook meals.

Karantina means "quarantine."
The suffix -dığından comes from:
• root başla- ("to start")
• past tense -dı → başladı ("it started")
• buffer -ğ + ablative -ından → başladığından ("from the fact that it started")
Then we add beri ("since"), yielding başladığından beri = "since it started."
So Karantina başladığından beri literally is "since quarantine started."

Why isn’t there a personal pronoun ben ("I") at the beginning of the sentence?

Turkish is a pro-drop language: you often omit subject pronouns because the person can be inferred. Here, fırsatım ("my opportunity") already tells you it's about "my" experience, so ben is unnecessary.

What does fırsatım oldu literally mean, and why do we use oldu ("became") here?

Fırsat- = "opportunity, chance" (noun)
-ım = first-person singular possessive → fırsatım = "my opportunity"
olmak = "to become" → oldu = "it happened/became"
Put together, fırsatım oldu literally means "my opportunity happened", i.e. "I had a chance."

Why is yemek pişirmeye in the dative case (with -e) instead of the plain infinitive pişirmek?

With expressions like fırsat(ım) oldu, the action you get a chance to do is marked by the dative -e. So the infinitive pişirmek ("to cook") becomes pişirmeye ("for cooking"). Together, yemek pişirmeye fırsatım oldu = "I had the opportunity for cooking food."

Could I use vaktim oldu ("I had time") instead of fırsatım oldu? Are they interchangeable?

Yes, they’re very similar.
• vaktim oldu = "I had time" (emphasizes having free time)
• fırsatım oldu = "I had a chance" (emphasizes the occasion or opening)
In everyday speech, both are used to mean "I found the time/chance to do something."

Why is Karantina capitalized here? It’s not a proper noun in Turkish.

Just like in English, the first word of a Turkish sentence is capitalized, regardless of whether it’s a common noun. Here Karantina is simply the first word.

Is there another way to say "since quarantine started" in Turkish?

Yes. You can also use the suffix -alı:
• Karantina başlayalı – literally "since quarantine has started."
However, -alı and -dığından beri aren’t used together. You’d say, for example:
• Karantina başlayalı yemek pişirmeye fırsat buldum.
Both mean "I’ve had the chance to cook ever since quarantine started," but -dığından beri is very common in writing and formal speech, while -alı is slightly more colloquial.