Bring 4 ½ cups water to a simmer in a large saucepan. Whisk in polenta and salt. Reduce heat to medium-low and cook, whisking often, until polenta thickens and begins to bubble, 5-10 minutes. Whisk in parmesan and butter; keep warm while you cook the shrimp.
Melt ¼ cup butter in a large skillet over medium heat. Add garlic, smoked paprika and chile flakes and cook until fragrant, about a minute. Increase heat to medium-high and add shrimp; season with salt and pepper. Cook on both sides until seared and pink, about 4 minutes total. Stir in remaining tablespoon of butter.
Divide polenta among four shallow bowls. Top each bowl with shrimp and warm butter sauce.
