Preheat the oven to 350°F. Prepare a 1.5 quart casserole dish by rubbing with a cut garlic clove (if desired) and coating with about a tablespoon of olive oil. Set aside.
Carefully slice potatoes to about ⅛ inch thickness, and tomatoes to about ¼ inch thickness with a mandolin or sharp knife. Set aside.
Heat 2 tablespoons of olive oil in a large pan over medium heat. Add onion, pepper, and garlic and sauté until onions are tender, about 4-5 minutes. Pour i in white wine (or water) and simmer until the liquid is reduced by about half.
Add sliced potatoes and water to pan. Cook for about 2-3 minutes until the liquid is slightly thickened, then stir in the chopped basil.
Pour potato mixture into prepared dish, and spread it out into an even layer. Sprinkle with sea salt. Carefully arrange tomato slices over top of potatoes. Sprinkle with salt and pepper and drizzle with about a tablespoon of olive oil.
Cool for 10 minutes before serving, or serve at room temperature.
Bake, uncovered, for about 1½ hours or until potatoes and tomatoes are tender, then remove from oven and sprinkle with cheese. Bake for another 10-12 minutes until bubbly and beginning to turn golden brown.
Cool for 10 minutes before serving, or serve at room temperature.