Learn Hardcore Japanese: watasi ha bangohan ni atarasii ryouri wo tukuritai desu.

In this sentence に marks the time or occasion when you want to do something—“at dinner.” If you used で, it would mean “at the place of dinner” (which sounds odd), and を can’t mark time. So 晩ご飯に = “for/at dinner.”

Why does 料理 take the particle を?

料理 (“dish; cooking”) is the direct object of the verb 作りたい (“want to make”), so it needs the object marker を to show what you want to make: 料理を作りたい = “want to make a dish.”

What is the ～たい form, and how does it work?

The ～たい form turns a verb into an adjective meaning “want to do [verb].” You take the verb’s stem (here 作り from 作る), add たい, and you get 作りたい = “want to make.” It behaves like an い-adjective (you can conjugate it for tense and politeness).

Why is there a です after 作りたい if たい is already an adjective?

Adding です makes the sentence polite. Since たい is treated like an い-adjective, you can append です for politeness:
• Casual: 作りたい。
• Polite: 作りたいです。

Can I drop 私は and just say 晩ご飯に新しい料理を作りたいです?

Yes. In Japanese you often omit the subject if it’s clear from context. Starting with 私 is fine but not required. Your listener will understand that “I” want to cook.

How do I say that I didn’t want to make it or that I wanted to make it (past)?

You conjugate the たい-adjective like any い-adjective:
• Negative: 作りたくないです = “I don’t want to make [it].”
• Past: 作りたかったです = “I wanted to make [it].”
• Past negative: 作りたくなかったです = “I didn’t want to make [it].”

Why use 新しい before 料理?

新しい is an い-adjective meaning “new.” In Japanese, adjectives come directly before the noun they modify, so 新しい料理 = “new dish.”

Could I use 作ります instead of 作りたいです to express “I want to cook”?

No. 作ります simply states “I will make” or “I make.” To express desire you must use the ～たい form. So 作りたいです is “I want to make.”