How to Make It
Place cashews in a bowl; cover with cool water by 1 inch. Cover bowl; refrigerate for at least 4 hours. Drain and rinse cashews. Place in a high-speed blender.
Bring a kettle of water to a boil. Place olive oil and garlic in a small unheated skillet. Turn heat to medium-low; cook, undisturbed, until garlic begins to sizzle. Let sizzle for 30 seconds, then transfer to blender. Add parsley, basil, oregano, lemon juice, 1/4 tsp. each salt and pepper, and 1 cup boiling water; blend until smooth (add more water if needed to reach desired consistency). Taste and season with additional salt and pepper, if desired.
Warm avocado oil in a large skillet over medium heat. Add beet noodles, season lightly with salt, and cook, tossing occasionally, until noodles reach desired degree of tenderness, 3 to 7 minutes. Divide among 4 bowls, top each with 1/4 cup sauce, sprinkle with pepper and parsley, and serve. (Cover and refrigerate leftover sauce for up to 3 days.)