Preheat the oven to 375 degrees . In a large skillet, heat the EVOO over medium. Add the onion and cook until softened, about 10 minutes; transfer to a plate. Place the tomato in the skillet in a single layer and cook, turning once, until softened at the edges, about 1 minute. Transfer to another plate.
In a bowl, stir the eggs, 1/4 cup parmigiano-reggiano, the basil and 1/2 tsp. salt to combine.
Spread the onion slices in the bottom of the skillet; pour the beaten eggs on top and cook over medium- low heat until the eggs are set around the edges, 2 to 3 minutes.
Place the tomato slices on top of the frittata; dollop the ricotta between the tomatoes. Sprinkle the remaining 1/4 cup parmigiano-reggiano on top. Bake the frittata until the top is golden and set, about 18 minutes. Let rest for a few minutes, then run a spatula around the edge of the skillet to slide onto a platter or cutting board. Cut into wedges. Serve warm or at room temperature.