Preheat the oven to 350 degrees.
Melt 3 tablespoons of the butter in a 10-inch oven-proof omelet pan over medium-low heat. Add the potatoes and fry them until cooked through, turning often, 10 to 15 minutes. Melt the remaining 5 tablespoons of butter in a small dish in the microwave.
Meanwhile, whisk the eggs in a large bowl, then stir in the ricotta, Gruyère, melted butter, salt, pepper, and basil. Sprinkle on the flour and baking powder and stir into the egg mixture.
Pour the egg mixture over the potatoes and place the pan in the center of the oven. Bake the frittata until it is browned and puffed, 50 minutes to an hour. It will be rounded and firm in the middle and a knife inserted in the frittata should come out clean. Serve hot.
Copyright 2002, Barefoot Contessa Family Style by Ina Garten, Clarkson Potter/Publishers, All Rights Reserved