僕には料理が得意。
is simply ungrammatical.
僕にはペンが必要です。
is grammatical only because 必要だ can take two arguments (AがBに) as word-specific feature, not that it's a universal grammar for adjectives. It's like the English word worth can have an object but most other adjectives can't.
Other adjectives that take に include ふさわしい (あなたが隊長にふさわしい) and 夢中だ (僕は君に夢中だ) etc., but basically you have to learn one by one.
And as already pointed out in comments above:
× 僕がペンを必要する。
僕がペンを必要にする。 → I make the pens necessary.
僕がペンを必要とする。 → I necessiate a pen.
na-adjective + にする
results in a verb "make ... adjective" and とする
"regard ... adjective".