Bring a large pot of salted water to a rolling boil, then add the pasta and cook for 8-10 minutes until just shy of al dente. Drain, reserving about ½ cup of pasta water, and set aside.
While the pasta cooks, heat olive oil in a large skillet over medium heat. Once shimmering, add the minced garlic and sauté for about 30 seconds until fragrant, the smell should be pungent and inviting, and the garlic should turn lightly golden.
Add the shrimp to the skillet in a single layer. Cook for 2-3 minutes per side until they turn pink, opaque, and have a slight curl. They should be juicy and firm—avoid overcooking to prevent rubberiness. Remove the shrimp from the pan and set aside.
Reduce the heat to low. Stir in the grated Parmesan cheese and lemon juice, stirring continuously until the cheese melts into a smooth, creamy sauce that coats the pan. If the sauce seems too thick, add a splash of the reserved pasta water to loosen it and bring it to a silky consistency.
Add the drained pasta to the skillet, tossing gently to coat it evenly with the cheesy sauce. Cook together for 1-2 minutes, allowing the flavors to meld and the pasta to absorb some of the sauce. If needed, stir in more reserved pasta water to loosen the sauce.
Return the cooked shrimp to the skillet, gently tossing everything together. Sprinkle with red pepper flakes if you like a bit of heat, and season with salt and pepper to taste. Squeeze fresh lemon over the dish for brightness, then give it a final toss.
Serve the pasta hot, garnished with additional Parmesan and a drizzle of olive oil if desired. The sauce should be silky, the shrimp juicy, and the pasta perfectly al dente—ready to enjoy immediately.
