Bring a large pot of salted water to a boil, then add the pasta and cook until al dente, about 8-10 minutes. Drain and set aside, reserving a cup of pasta water.
While the pasta cooks, peel and devein the shrimp if needed, then pat them dry and season lightly with salt and pepper.
Heat a large skillet over medium heat, then add a tablespoon of olive oil and a tablespoon of butter. Once melted and shimmering, add the shrimp.
Sauté the shrimp for 2-3 minutes per side until they turn pink and opaque, with a slight caramelization on the edges. Remove shrimp from skillet and set aside.
In the same skillet, add the minced garlic and cook for about 30 seconds until fragrant and golden, being careful not to burn it.
Pour in the heavy cream and bring to a gentle simmer, stirring constantly until the sauce begins to thicken slightly, about 2 minutes.
Gradually stir in the grated Parmesan cheese until melted and smooth. Add lemon juice and stir to combine, then taste and adjust seasoning with salt and pepper.
Return the cooked shrimp to the skillet, stirring gently to coat them with the sauce.
Add the cooked pasta to the skillet, tossing gently to combine everything evenly. If the sauce is too thick, loosen it with a splash of the reserved pasta water until glossy and coats the pasta beautifully.
Finish with a squeeze of fresh lemon juice for brightness, then give everything a final gentle toss.
Serve immediately, garnished with extra Parmesan or chopped herbs if desired, while the sauce is silky and hot.