Heat 3 tablespoons of olive oil over medium heat in an oven-safe skillet, and cook and stir the onion and garlic until translucent, about 5 minutes. Stir in the green peppers, and cook and stir until they have begun to soften, 5 more minutes. Pour the eggs over the vegetables, and stir in the basil, rosemary, salt, and pepper. Reduce the heat to medium-low, let the eggs sit over the heat until they have started to set, about 10 minutes.
Transfer the skillet to the preheated oven and cook the frittata until fully set, about 15 minutes.
While the frittata is baking, heat 1 cup of olive oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C). Deep-fry the sweet potato slices, a layer at a time, until golden brown and crisp, about 5 minutes. Remove with a slotted spoon, and drain on paper towels. Top baked frittata with the fried sweet potato slices to serve.