In a large skillet or dutch oven, heat olive oil over medium heat. Once hot, sauté mushrooms, onion and garlic until the mushrooms have cooked out and absorbed their liquid, approximately 6-7 minutes. Add a splash of stock to deglaze the pan and scrape up any browned bits from the bottom of the pan with a wooden spoon. You may also want to bring a large pot of water to a boil now if you're making pasta to go with your bolognese sauce.
Add the fresh thyme, carrots, celery and a pinch of salt and pepper (and red pepper flakes, if using), cooking for another 3-5 minutes stirring often to avoid any chance of burning. Add a splash of stock to deglaze the pan again.
Stir in the stock and crushed tomatoes. Allow to simmer lightly for an additional 15 minutes, stirring occasionally.
When carrots are tender to the touch, pulse the bolognese a few times with an immersion blender to create a chunky texture and thicken the sauce. If you don't have an immersion, add 3-4 scoops of the sauce to a blender or food processor, pulse a few times, then pour back in with the rest of the sauce.
Season with salt and pepper. Serve bolognese over your favourite cooked pasta, topped with fresh basil or parsley and vegan parmesan.