Preheat oven to 375F and line a medium sheet pan with parchment paper or lightly grease.
Toss broccoli florets, olive oil, and lemon juice together until coated. Spread broccoli in an even layer and season with salt and pepper. Roast broccoli at 375F 15-20 minutes until broccoli is tender. Set aside.
In a medium bowl, whisk egg yolks, egg, Parmesan, and lemon zest until completely smooth. Set aside.
Bring a pot of water to a boil and salt. Add pasta and cook until just barely al-dente. Reserve 1-1/2 cups pasta cooking water and drain pasta.
Melt butter in a large high-walled skillet over medium heat. Add garlic and sauté 1-2 minutes until fragrant. Add pasta and 1/2 cup reserved pasta water to garlic mixture. Cook over medium heat 2-3 minutes until liquid is absorbed. Remove from heat and allow to cool 2 minutes.
Whisk 1/4 cup pasta water into egg mixture until smooth. Fold egg sauce into hot pasta mixture, stirring constantly with a wooden spoon until a creamy sauce forms and coats pasta (drizzle in additional pasta water if needed to loosen sauce).
Toss broccoli and parsley into carbonara and season with salt and pepper to taste. Serve carbonara immediately while hot with additional Parmesan grated on top. Enjoy!