Step 1Brush the bread slices with clarified butter or olive oil. Toast the bread in a large skillet over medium-high heat until browned on both sides, 5 to 6 minutes. Rub each slice with the cut garlic clove and set aside.
Step 2Whisk together the eggs, 1 tablespoon butter cut into small pieces, the salt and white pepper.
Step 3Melt the remaining 1 tablespoon butter in a 9-inch nonstick skillet over low heat. Add the eggs and cook, stirring occasionally, until they begin to set on the bottom, about 2 minutes.
Step 4Continue to cook, stirring almost constantly, until the eggs become creamy, with a texture resembling small-curd cottage cheese. Continue cooking and stirring until they begin to thicken and become less glossy but are not quite done, 8 to 15 minutes.
Step 5Remove the eggs from the heat and stir for about a minute to finish the cooking. They should be very creamy, with very small curds.
Step 6Divide the eggs onto the toasted bread and spread over each slice. Top each serving with a slice of prosciutto.