Preheat your oven to 375°F (190°C).
Peel and dice the potatoes into small cubes.
Melt 2 tablespoons of butter in a medium saucepan over medium heat. Add the diced potatoes and sauté for about 10-15 minutes until golden brown and tender.
In a large mixing bowl, whisk together the eggs, ricotta cheese, and the remaining 4 tablespoons of melted butter. Add grated cheddar cheese, chopped chives, and fresh basil. Season with salt and black pepper, and mix until combined.
In a separate bowl, whisk together the flour and baking powder. Gradually add this to the egg mixture, stirring until just combined.
Gently fold the sautéed potatoes into the egg mixture until evenly distributed.
Grease your sheet pan and pour the frittata mixture into it. Spread evenly and bake for 25-30 minutes until the top is set and golden brown.
Let the frittata cool for about 10 minutes, then slice into squares for serving.