Bring a large pot of salted water to a boil and cook the pasta until just al dente, about 8 minutes. Reserve ½ cup of pasta water, then drain and set aside.
While the pasta cooks, peel and devein the shrimp if needed. Pat them dry with paper towels to prevent splattering during cooking.
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat until shimmering, then add the shrimp. Sear for 2-3 minutes per side until pink and lightly charred, then remove and set aside.
In the same skillet, add the chopped garlic and red pepper flakes. Toast for about 30 seconds until fragrant and golden, stirring constantly to avoid burning.
Return the cooked shrimp to the skillet, then add the drained pasta. Toss everything together over medium heat, letting the flavors mingle and adding a splash of reserved pasta water if the mixture seems dry and sticky.
In a small bowl, whisk together the eggs and grated Pecorino Romano cheese until smooth and creamy.
Remove the skillet from heat, then quickly pour in the egg and cheese mixture. Toss vigorously to create a silky, emulsified sauce that coats the pasta evenly. If needed, add a little more reserved pasta water to loosen the sauce.
Taste and adjust seasoning with salt, black pepper, and a squeeze of lemon juice if using. Toss again to combine everything well.
Serve immediately, garnished with extra Pecorino Romano and a drizzle of good olive oil if desired. Enjoy the creamy, smoky, seafood-infused pasta while hot.
