Cut zucchini lengthwise into 1/4-inch-thick slices. Brush zucchini with 1 tablespoon olive oil. Sprinkle with salt. For a charcoal grill, place zucchini directly over medium coals. Grill, uncovered, for 4 to 6 minutes or until crisp-tender, turning once. (For a gas grill, preheat grill. Reduce heat to medium. Place zucchini on grill rack directly over heat. Cover and grill as above.) Set zucchini aside.
In a food processor or blender, cover and process shallot and garlic until chopped. Add cottage cheese, 2 tablespoons olive oil, black pepper, and nutmeg. Cover and process or blend until nearly smooth. Set aside.
In a large bowl beat together eggs and milk. Stir in spinach, dried tomatoes, cottage cheese mixture, 1/2 cup of the Parmigiano Reggiano cheese, and 1/2 cup of the Pecorino Romano cheese.
Place 1-1/2 cups of the egg mixture in a greased 9-inch round baking pan. Top egg mixture with grilled zucchini, cutting to fit. Add remaining egg mixture. Sprinkle with remaining 1/4 cup each Parmigiano Reggiano and Pecorino Romano cheese.
For a charcoal grill, arrange medium-hot coals around edge of grill. Test for medium heat above center of grill. Place pan on grill rack in center of grill. Cover and grill about 35 minutes or until a knife inserted near center comes out clean. (For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking. Cover and grill as above.) Or, bake in a 375 degree F oven about 35 minutes or until a knife inserted near center comes out clean. Let stand at least 20 minutes before cutting.
Serve warm or at room temperature with a simple green salad. Cover and chill to store. Makes 6 to 8 servings.