Pat the shrimp dry with paper towels. In a medium bowl, toss the shrimp together with the smoked paprika and a small pinch or so of salt and pepper.
Bring a large pot of lightly salted water to a boil. Add the pasta and cook until al dente, according to package directions. BEFORE DRAINING, ladle out 1-2 cups of the pasta water and set aside for later. Drain the pasta.
While the pasta is cooking, heat the 1 tablespoon butter + 1 tablespoon olive oil in a 12-inch skillet (or a deep skillet) over medium heat until hot and rippling. Add half of the shrimp in a single layer and cook for 30-45 seconds; flip the shrimp and cook just until the shrimp have turned pink and are cooked through (it won't take long!).
Using tongs, remove the shrimp to a plate keeping as much butter/liquid in the pan as possible. Repeat with remaining shrimp – removing to the plate with the other shrimp when done cooking.
Return the pan to medium heat and melt the 2 tablespoons butter. Add the garlic and cook, stirring often (don't let it burn!), until fragrant, about 30-45 seconds.
Pour the heavy cream into the pan and whisk to combine, letting the sauce bubble and thicken slightly, 1-2 minutes.
Add the salt, pepper and Parmesan cheese. Stir over medium heat until the cheese is melted.
Add the cooked noodles, lifting and tossing with tongs to coat the pasta thoroughly with the sauce. Add spoonfuls of the reserved pasta water to loosen the sauce and pasta (just eyeball it – probably won't need to add all the reserved water).
Add the shrimp and toss to combine with the pasta. Season to taste with additional salt and pepper, if needed! Sprinkle with fresh parsley.
Serve immediately.
Serve with additional Parmesan cheese, if desired.
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