Bring a pot of lightly salted water to a boil. Cook egg noodles in the boiling water, stirring occasionally until cooked through but firm to the bite, about 5 minutes. Drain and transfer noodles to a bowl.
Stir sriracha sauce, butter, peanut oil, rice vinegar, basil, paprika, and black pepper together in the same pot over medium heat until sauce is smooth and heated through, 3 to 5 minutes. Add noodles to sauce and toss to coat. Cool before serving.
