Preheat the oven to 350 degrees F (175 degrees C). Grease a 1 1/2-quart casserole dish.
Combine cherry tomatoes, basil, garlic, red wine, and 1/8 teaspoon salt for marinara in the bowl of a food processor. Pulse a few times to puree. Set aside.
Bring water and 1/2 teaspoon salt to a boil in a medium saucepan over medium-high heat. Whisk in polenta slowly, whisking constantly to ensure there are no lumps. Bring back to a boil; reduce heat to low and cook, stirring occasionally, for 5 minutes. Remove from heat and stir in Pecorino Romano cheese and butter.
Pour 1/2 of the polenta into the prepared casserole dish. Top with 1/2 of the sliced zucchini, overlapping slices slightly. Top zucchini with 1/2 of the marinara sauce, then sprinkle with 1/2 of the Italian-style cheese. Repeat layers one more time.
Bake, covered, in the preheated oven for 30 minutes. Uncover and continue to bake until cheese on top is slightly brown, about 10 minutes more. Remove from the oven and let stand for 5 minutes before serving.