Preheat oven to 350°F. Spray a 9 x 13-inch baking dish with cooking spray and set aside.
Cook egg noodles in a large pot of well salted boiling water, just until al dente, according to package directions. Drain.
While the noodles are cooking, whisk together condensed soups, milk, and optional sour cream, garlic powder, and onion powder (if using) in a large bowl.
Stir in the noodles, ham, and vegetables (if using). Taste and season with salt and pepper, if desired.
Transfer the noodle mixture to the prepared baking dish. Cover tightly with foil.
Bake, covered, for 25-30 minutes, until the filling is hot and bubbly.
Remove the cover, sprinkle the cheese on top, and return the dish to the oven (uncovered) for 5-10 more minutes, just until the cheese melts.