Bring a large pot of salted water to a boil. Add the pasta and cook according to the package instructions for al dente. Drain and set aside.
Meanwhile, melt the butter in a large skillet over medium heat. Stir in the garlic, red peppers and paprika and cook, stirring occasionally, until the peppers are heated through and the butter is fragrant and vibrant red, about 2 minutes. Add the cream and bring to a boil. Reduce the heat to medium low and simmer, stirring occasionally, until slightly thickened, 3 to 4 minutes.
Add the shrimp and cook until they are firm and cooked through, about 5 minutes. Add the cooked pasta, Parmesan and 1 teaspoon salt and toss until well coated (see Cook's Note). Sprinkle with parsley.
Don't worry if it seems like there is too much sauce. As soon as everything is tossed together, the sauce will start to cling to the pasta and thicken before your eyes.
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