The state health codes applicable to food are here esp. ch. V and here. The primary focus of those health codes is preventing the introduction of toxic substances or pathogens. There is obviously no law against serving meat, nor is there any law against half-and-half pizza. The only possible prospect for a health law addressing your interest would be via the allergy avenue (yes, you do not allege to be allergic to anything – my point is that even if you did, this would not help your cause). There are some provisions regarding training and informing when it comes to "major food allergens", which however is defined as
Milk, EGG, FISH (such as bass, flounder, cod, and including crustacean
shellfish such as crab, lobster, or shrimp), tree nuts (such as
almonds, pecans, or walnuts), wheat, peanuts, and soybeans
or proteins derived from the above. Note that mammal meat is not included (it may be an individual allergen, but it is not a statutory major food allergen).
Even if you wanted to sue, you would have a very hard time establishing that you were damaged. First you would have to establish that they have a legal obligation to serve you "vegetarian food" (crucially undefined). You might be able to establish that they made such a promise. Now we have to determine whether a reasonable person would conclude that a pie with half-meat and half non-meat is clearly not vegetarian food. I do not believe that there is secular case law addressing this, so the courts would resolve this by determining whether there is a reasonable means for a vegetarian to eat part of such a pizza – obviously, yes, only eat the cheese part (leave wide margins).
So there is no legal recourse for getting what you want: there are still ample political options.