Warm a heavy pot over medium heat; add oil and butter until melted.
Sauté onion, carrots, and celery until softened and lightly golden, about 7 minutes.
Stir in mushrooms and sweet potato; cook, stirring, until mushrooms release moisture, 5 minutes.
Add garlic, thyme, rosemary, and crushed bay leaf; cook until fragrant, 1 minute.
Sprinkle in flour; stir constantly to coat vegetables and cook off raw taste, 1 minute.
Pour in broth and add wild rice; scrape up browned bits, bring to a boil.
Reduce heat, cover, and simmer gently until rice is tender, 45–55 minutes, stirring occasionally.
Stir in half-and-half; simmer until slightly thickened, 3–5 minutes; season with salt and pepper.
Finish with vinegar and parsley; let stand 5 minutes before serving.