Preheat the oven to 400 degrees.

Place the broccoli on a baking sheet and drizzle with the olive oil. Sprinkle with pepper and salt. Roast for 15-20 minutes or until nicely browned, turning the broccoli once during cooking.

While the broccoli is cooking, add the bacon to a large saute pan and cook until browned. Remove the bacon from the pan and drain on a paper towel lined plate.

Mix the black pepper, egg, egg yolks, and 3/4 cup Parmesan cheese together in a medium bowl. Add the bacon and set aside.

Cook the pasta according to package directions. Drain, reserving 1 cup of pasta water.

Place the drained pasta in the skillet that held the bacon. Add 1/4 c. pasta water and the egg mixture. Stir vigorously to prevent the eggs from solidifying.

Continue to add pasta water a few tablespoons at a time until a creamy sauce forms.

Add the broccoli to the pasta and toss to coat.

Serve pasta with remaining Parmesan cheese.