Boil a large pot of salted water. Cook udon until just tender, reserving 1/2 cup cooking water. Drain.
Heat oil and butter in a large skillet over medium-high. Add mushrooms, salt, and pepper. Sauté until browned, 4–5 minutes.
Stir in garlic and cook 30 seconds until fragrant.
Whisk in gochujang, soy sauce, mirin, and honey. Cook 1 minute to bloom the paste.
Pour in broth and heavy cream. Simmer 2–3 minutes, stirring, until slightly thickened.
Add cream cheese. Stir until fully melted and the sauce is smooth.
Toss in drained udon. Add a splash of cooking water if needed so the sauce coats the noodles.
Finish with sesame oil, rice vinegar, and green onions. Sprinkle sesame seeds and adjust seasoning. Serve hot.