That the OP mentions a specific dish "Mushroom Tortellini" leads me to believe this is pre-ordering for J (or maybe W if they ever brought that back?) and not a standard special meal.

There is no "special vegetarian menu". When flying in the premium cabins, there is usually one vegetarian option, though if you don't pre-order it you run the (relatively low) risk of it running out before they get to your seat. Alternately, you can pick an appropriate "special meal" (VGML, VLML, AVML, etc), though in the premium cabins these tend to be lower quality.

So basically:

• In a premium cabin, you can pick a pre-order option if there's one you like. Or you can request a special meal, but you won't know what the actual entree will be until they hand it to you. Sometimes it's the same as the vegetarian option on the pre-order menu.
• In the main cabin, your only way to guarantee vegetarian is to request a special meal. Depending on which one you pick, it might be one of the regular options they would have offered anyway.
• If you don't pre-order OR pick a special meal, you will probably still be able to get whatever vegetarian option they have on board, but they might run out, and in some cases (though much less common than it used to be) there might not even be a vegetarian option.

I have no idea where you can put in your profile that you prefer vegetarian meals. I don't see this anywhere in the Delta preferences or profile.