In an oven safe frying pan, add all ingredients but the eggs. Bake for 35-40 minutes, stirring every 10-15 minutes.
Once the carrots are soft, take the pan out of the oven and make 2 "cups" for the eggs to go in. Crack one egg in each cup, and put pan (covered now) on the oven over medium high heat. Cook the eggs for about 5 minutes, until the whites are cooked and the yolk is still a little runny.
Season with more pepper before serving.
Makes 2 servings. Enjoy!