Wash the fish and pat dry, season with salt and pepper. Cook pasta in boiling salted water according to package instructions. Heat 1 tablespoon of oil in a pan, sauté the thyme briefly in it, remove.
Add 2 tablespoons of oil to the hot pan. Fry the fish for 3-4 minutes on each side. Drain the pasta, drain and mix with pesto and thyme. Season to taste with pepper. Arrange pesto noodles with fish and serve.