Preheat oven to 425 degrees F (220 degrees C).
In a large baking dish, toss the red potatoes with 1/2 the olive oil, garlic, rosemary, thyme, and 1/2 the kosher salt. Cover with aluminum foil.
Bake 20 minutes in the preheated oven. Mix in the asparagus, remaining olive oil, and remaining salt. Cover, and continue cooking 15 minutes, or until the potatoes are tender. Increase oven temperature to 450 degrees F (230 degrees C). Remove foil, and continue cooking 5 to 10 minutes, until potatoes are lightly browned. Season with pepper to serve.