The modifier "As the next manager of Pizza Perfection" is a dangling modifier.
A dangling modifier is a grammatical construct that is ambiguous, for it is not clearly and logically conected to the word it is intended to modify. Therefore, it can be confused as a modifier of a word other than the one intended, or of no word at all. In the case at hand, the phrase seems to be modifying the subject, "you", when, in reality, it is refering to the speaker.
A good correction would be, for example:
"You said you wanted thicker crusts and cheesier pizzas. As I am the next manager of Pizza Perfection, you will get pizza as near to perfect as we can make it."