I looked up something similar in reference to rotir, and in that case also, rotir or faire rotir were considered equally correct. There was clearly difference of opinion on language sites and in the forums. 

Link is from Larousse :

DIFFICULTÉS

EMPLOI

On dit couramment faire cuire qqch ou mettre à cuire qqch, mais cuire qqch ou mettre cuire qqch sont également corrects : faire cuire un rôti ; mettre à cuire un gâteau ; cuire des pommes de terre, du pain ; mettre cuire au four.

(My wife - French - wouldn't use faire cuire in this context).