Bring a large pot of salted water to a boil for the pasta.
Warm olive oil and vegan butter in a wide skillet over medium heat. Add onions and 1/2 teaspoon salt; cook, stirring often, for 10 minutes.
Lower heat to medium-low. Continue cooking until onions turn deep golden and jammy, 20–25 minutes, stirring occasionally.
Stir in garlic, dried thyme, and red pepper flakes. Cook 1 minute until fragrant.
Deglaze with balsamic vinegar, scraping up browned bits. Pour in vegetable broth and oat milk; simmer 3–4 minutes to slightly thicken.
Stir in nutritional yeast and black pepper. Taste and add more salt if needed.
Cook pasta until al dente. Reserve at least 1/2 cup pasta water, then drain.
Toss pasta into the onion sauce over low heat, adding splashes of reserved water until glossy and well-coated.
Finish with lemon juice and parsley. Serve immediately.