Boil angel hair in well-salted water for 2 minutes. Reserve 1/2 cup pasta water before draining. Drizzle with a little olive oil to prevent sticking and set aside.
Seafood
In a wide skillet over medium-high heat, melt butter and let it cook until it turns amber and smells nutty. Add shrimp and mussels together. Toss and cook just until shrimp are pink and mussels have opened, 2-3 minutes. Remove everything and set aside. Discard any mussels that have not opened.
Sauce
In the same pan over medium heat, add butter. Add garlic, chili flakes, and lemon zest. Cook 30 seconds until garlic is just golden. Add white wine and let reduce by half, about 2 minutes. Add lemon juice and season with salt and pepper.
Finish
Add angel hair directly to the sauce and toss until fully coated. Add a splash of pasta water if it tightens too fast. Nestle shrimp and mussels back in and toss gently once to combine.
Plate
Twirl pasta into a wide shallow bowl. Arrange mussels around the top with open shells facing up. Scatter parsley and extra lemon zest over everything. Finish with chili flakes and lemon wedges on the side.
Notes
The browned butter is the flavor base. Let it go fully amber before adding the seafood as it adds a nutty depth the sauce needs.
Mussels and shrimp go in together since they cook at roughly the same speed. Don't overcook and pull them the moment the mussels open.
Angel hair overcooks in seconds. It finishes in the sauce so pull it early from the boil.