Preheat the oven to 180°C.
Cut the bagel in half. Using a knife or cookie cutter make the hole a bit bigger so that cracked egg can easily fit in there.
Lightly grease the cut side of the bagels with pesto or dairy-free spread, then lay the prosciutto on top, covering the hole. Push the prosciutto using the sundried tomatoes, creating a little nest for the egg.
Move the bagel nests onto a greased or lined baking tray, then crack the eggs into the holes. Season with pepper, then bake for 10-15 minutes depending on how well-done you like your fried egg.
Serve warm with a crunchy salad.