Preheat oven to 350 degrees. Line a baking sheet with parchment paper or aluminum foil. Use a sharp knife to slice the top quarter off each pumpkin; remove the seeds and stringy pulp.
In a medium frying pan, break up and fry the sausage until thoroughly cooked, 5–6 minutes. Remove from heat, drain grease, and cool to room temperature.
In a large bowl, whisk 1 egg until foamy. Add the sausage, bread cubes, parsley, sage, salt, and pepper; stir until well combined. Fill each pumpkin with the bread mixture to about 1 inch from the top; transfer to the prepared baking sheet. Bake until the pumpkins are fork tender, 40–45 minutes. Remove pan from oven and use a spoon to gently flatten the stuffing in each pumpkin.
Increase oven temperature to 400 degrees. Crack 1 egg and gently pour it over the stuffing mixture for each pumpkin, being careful not to break the yolk; sprinkle each with 1 teaspoon cheese. Cover the pumpkins lightly with foil, return to oven, and bake until eggs are set to desired doneness, 10–13 minutes.