Preheat the oven to 400 degrees F.
Heat 2 tablespoons of the oil in a 8 to 10-inch skillet or saute pan. Add the onion, and cook slowly until the onion is wilted and translucent. Add the hot sauce. Add the tomatoes, raise the heat, and cook for several minutes, stirring, or until the liquid has evaporated. Drain off the fat and transfer the tomatoes and onions to a bowl. (If desired, add well-drained artichoke hearts here.) Mix in salt and pepper, then cheese and basil.
In a bowl, beat the eggs with salt and pepper until blended, but not smooth. In a well-seasoned 8 to 10-inch skillet (non-stick works well), heat the remaining 2 tablespoons oil. Arrange the tomato and onion mixture in the bottom of the skillet, and pour the eggs over the top, pressing the top down with a fork so the solids are covered. Stir a little. Cook over medium heat until the eggs begin to bubble gently around the edges.
Immediately place the frittata in the center of the oven and cook until it is puffy and set in the center, about 10 minutes. Slide out onto a serving plate. Serve immediately or set aside and serve at room temperature. Serve with a dollop of sour cream and more hot red pepper sauce.