Bring a large pot of salted water to a boil and cook the pasta until al dente according to package directions, reserving about 1/2 cup of the pasta cooking water before draining.
While the pasta cooks, melt the butter in a skillet over medium heat.
Add the minced garlic and crushed red pepper flakes (if using) to the melted butter and cook, stirring, for about 1 minute until fragrant but not browned.
Turn off the heat, add the drained pasta to the skillet, then stir in the grated Parmesan and the chopped parsley, basil, and chives.
Add a splash (a few tablespoons) of the reserved pasta water and toss continuously until the cheese melts and the pasta is evenly coated; add more pasta water as needed to reach the desired sauce consistency.
Season generously with salt and freshly ground black pepper, toss once more, and serve immediately with extra Parmesan if desired.