Spaghetti and Broccoli with Carbonara Sauce

Name: Spaghetti and Broccoli with Carbonara Sauce
Ingredients: 1 large egg plus 2 egg yolks; 1⁄4 cup heavy cream; salt and freshly ground black pepper; 8 oz. bacon or pancetta, finely chopped; 2 1⁄2 cups small broccoli florets; 1 clove garlic, finely chopped; 1⁄2 lb. dry spaghetti; 3 tbsp. grated Grana Padano cheese, plus more for garnishing