Cook spaghetti in well-salted water until 1 minute shy of al dente; reserve 1.5 cups pasta water, then drain.
Warm olive oil in large skillet over medium-low; add sliced garlic and cook 3-4 minutes until golden like honey, not brown.
Stir in red pepper flakes; cook 15 seconds.
Add drained pasta and 1 cup pasta water; toss vigorously over medium heat 1-2 minutes until oil and water emulsify into a glossy sauce coating the noodles.
Remove from heat, toss with parsley, season with salt, serve immediately.