Heat a medium non-stick frying pan over medium heat. Spread a thin layer of pesto across the pan and warm for 1-2 minutes until the color deepens.

Carefully crack the eggs into the warm pesto, ensuring they do not overlap. Sprinkle with salt, pepper, and red pepper flakes, and cook for 4-5 minutes.

Toast the sourdough slices until golden brown. Spread goat cheese on top to melt slightly from the warmth of the bread.

Lift the cooked eggs from the pan onto the sourdough toast. Spoon additional pesto over the eggs and serve immediately.