Preheat the oven to 375°F. In a small saucepan, bring 2 cups water to a boil.
Smear the bottom of each ramekin with the butter. For each serving, crack 2 eggs into a small bowl or dish, being careful not to break the yolks, then slide into a prepared ramekin. Season with the salt and pepper, drizzle with 1 tablespoon of the cream, and sprinkle with 1 tablespoon of the Parmesan. Set the ramekins into a medium-sized glass or ceramic baking pan, allowing at least 1 inch of space between dishes. Transfer to the bottom rack of the oven and pour the boiling water into the baking dish, being careful not to splash any hot water into the ramekins. Cover with a sheet of aluminum foil and bake 8 to 12 minutes, until the whites are set but the yolks are still soft and a bit runny. Prepare the piperade while the eggs are baking.
In a large skillet over medium heat, cook the prosciutto in the olive oil until beginning to crisp, then add the onion. Saute until lightly golden, then add the red and green pepper and cook until the strips just begin to soften. Add the garlic and cook 30 seconds to 1 minute, until fragrant, then add the tomatoes and red pepper flakes, if using. Allow the mixture to stew over medium-low heat until liquid has evaporated and the tomatoes are heated through. Check for seasoning and add salt and pepper. Off the heat, add the basil. Divide between the ramekins (you will have extra) and serve on a small plate, piping hot.
This recipe was provided by a finalist, who may or may not be a professional cook, for "The Next Food Network Star." Food Network has not tested this recipe and therefore cannot make representation as to the results.