Roast the garlic: Heat the oven to 400°F (200°C). Slice the top off the garlic head to expose the cloves.
Place on foil, drizzle with 1 tablespoon olive oil, and wrap tightly. Roast for 35–40 minutes until soft and golden. Let cool, then squeeze out the cloves.
Toast the breadcrumbs: In a skillet over medium heat, warm 1 tablespoon olive oil.
Add breadcrumbs with a pinch of salt and cook, stirring, until golden and crisp, 3–5 minutes. Transfer to a bowl and mix in half the lemon zest. Set aside.
Cook the pasta: Bring a large pot of salted water to a boil.
Cook pasta until just shy of al dente. Reserve 1 1/2 cups pasta water, then drain.
Build the sauce base: In a large skillet, melt butter with remaining 1 tablespoon olive oil over medium-low heat. Mash in the roasted garlic with a fork.
Add red pepper flakes if using. Cook 1–2 minutes until fragrant.
Toss with pasta: Add cooked pasta to the skillet with 3/4 cup reserved pasta water. Toss over medium heat until the sauce starts to cling.
Add Parmesan and lemon: Sprinkle in Parmesan gradually, tossing constantly.
Add more pasta water as needed to keep it glossy and silky. Finish with lemon juice and remaining lemon zest. Season with salt and plenty of black pepper.
Finish and serve: Off the heat, toss in parsley.
Plate the pasta, top generously with crispy breadcrumbs, and add extra Parmesan to taste.