Toast the bread until golden, then drizzle with olive oil and set aside.
Warm the pesto in a nonstick skillet over medium-low heat until it gently sizzles.
Crack in the eggs and let them settle, nudging pesto around the whites.
Cover the pan and cook until the whites set and yolks are jammy, 2–3 minutes.
Season with salt, black pepper, and red pepper flakes. Sprinkle with Parmesan.
Slide the eggs over the toast and spoon any extra pesto from the pan on top.