Place a medium nonstick skillet over low heat and add the basil pesto.
Warm the pesto gently until it begins to shimmer and lightly bubble. Avoid using high heat, which can scorch the basil and garlic.
Crack the eggs directly into the warm pesto, leaving a little space between them.
Cover the skillet and cook over low heat for approximately 2 minutes, or until the egg whites are set and the yolks have reached your preferred doneness. Cook a little longer if you prefer firm yolks.
Season the Pesto Eggs lightly with salt, black pepper, and red pepper flakes or Aleppo pepper.
If using toast, spoon a little warm pesto from the skillet over each toasted bread slice.
Arrange the sliced tomato and fresh mozzarella over the toast.
Carefully slide the cooked eggs over the tomato and mozzarella.
Spoon the remaining warm pesto from the skillet over the eggs and serve immediately