Heat olive oil and butter in a large Dutch oven or heavy pot over medium-high heat. Add mushrooms in a single layer (work in batches if needed) and cook without stirring for 4-5 minutes until browned. Stir and continue cooking until all mushrooms are golden, about 5 more minutes. Transfer to a plate.
Reduce heat to medium. Add onion, carrots, and celery to the pot; cook, stirring occasionally, until softened, about 8 minutes. Add garlic and tomato paste; cook for 1 minute.
Pour in the red wine, scraping up any browned bits from the bottom. Bring to a boil and let reduce by half, about 5 minutes.
Add vegetable broth, thyme, bay leaves, soy sauce, and the cooked mushrooms. Bring to a simmer, then reduce heat to low. Cover and cook for 30 minutes, stirring occasionally.
In a small bowl, whisk flour with 2 tablespoons water to make a slurry. Stir into the stew and cook uncovered for 10 more minutes, until thickened. Season with salt and pepper to taste.
Remove thyme sprigs and bay leaves. Serve over mashed potatoes, egg noodles, or with crusty bread. Garnish with parsley.
Tips
For a deeper flavor, use a mix of wild and cultivated mushrooms.
This stew tastes even better the next day; refrigerate overnight and reheat gently.
To make it gluten-free, use tamari and a gluten-free flour blend.