。
She insisted on cooking it her own way.
Literal
She [topic-は] no-matter-what it [object-を] [self-style-自己流] [adverbial-に] [wanted to-cook-料理したがった].
自己流 (jikoryū) literally 'self-style,' is a slightly self-deprecating noun meaning 'one's own (untaught/unconventional) way' — used both with pride ('I figured this out myself') and disclaim ('this is just my own approach, take it with a grain of salt'). Pairs with the adverbializer に: 自己流に料理する ('cook in one's own way'). たがる is the third-person desiderative auxiliary — 'X wants to (as observed from outside)'; you don't normally say たい about other people in Japanese, since you can't access their inner state, so たがる is the proper observational form.