Bake in an oven-safe skillet (10 or 12 inch is best) for 25 minutes, flipping once during cooking to promote even browning.
Push sweet potatoes aside to clear out three 2 inch diameter circles. Crack eggs into the circles.
Place skillet back in oven and bake for 5 more minutes, or until eggs are set to your desired level (if you leave them in the pan after removing from oven, they will continue to cook.)
Top skillet with diced avocado, salt, and pepper. Serve immediately.
For an alternate method of cooking the potatoes, place on a separate baking sheet for the initial cook (we love the Williams-Sonoma Gold Touch). Transfer to a preheated skillet when time to add the eggs. This can help give the potatoes a little bit nicer exterior "crunch".