Bring a large pot of salted water to a boil. Cook angel hair pasta until al dente. Reserve ½ cup pasta water before draining.
In a dry skillet over medium heat, toast walnuts, sage, and thyme for 3–5 minutes until fragrant and lightly golden. Remove and set aside.
Reduce heat to medium-low and add butter to the same pan. Stir continuously until butter turns deep golden brown and smells nutty, about 3 minutes. Remove from heat immediately.
Add pasta back to the pot along with grated cheese, black pepper, browned butter, and toasted walnut mixture. Toss well.
Add reserved pasta water a splash at a time until the sauce becomes silky. Plate and garnish with extra cheese and black pepper.
Notes
Keep a close eye on the pan while browning the butter! It can quickly go from a lovely nutty brown to burnt (which is not so lovely).
Reserve some pasta water before draining the pot. You will use it to create the sauce.
Freshly grated cheese melts better than pre-shredded.
Store any leftovers in an airtight container in the fridge for up to 3 days.