Combine garlic and 3 tbsp olive oil in a small bowl. Heat a large Dutch oven over medium and pour in garlic and oil. Add red pepper flakes and 2 tbsp butter; cook, stirring occasionally, until garlic is very fragrant but not browned, about 3 minutes. Add wine, increase heat to medium-high, and bring to a boil. Cook, uncovered, until reduced by 2/3, about 20-25 minutes. Season with salt and pepper
Meanwhile, cook pasta in a pot of salted water, stirring occasionally, until very al dente, about 3 minutes shy of recommended cooking time
Drain pasta and add to sauce with remaining 14 tbsp butter. Set pot over medium heat and bring sauce to a simmer. Cook, tossing often, until pasta is well-coated and sauce is thickened, about 3 minutes. Taste and season with more salt as needed
Divide among bowls, drizzle with olive oil, and top with Parmesan