In a large pot, heat 1 tablespoon of olive oil over medium heat, then add the mushrooms and a pinch of salt. Sauté for 8-10 minutes, until browned and softened. Transfer the mushrooms to a plate nearby.
To the pot, add another tablespoon of olive oil, along with the carrots and onions. Sauté for about 5 minutes, then add the garlic and cook for 1 more minute, until fragrant.
Pour the red wine and broth into the pot with the carrot/onion/garlic mixture and stir. Now add the tomato paste, thyme, oregano, salt and black pepper. Stir to combine and bring to a boil. Lower the heat and simmer, covered, for 15 minutes.
In a measuring cup or small bowl, stir the flour and water together, then add to the pot and stir well to thicken the sauce.
Add the cooked mushrooms back to the pot. Cover and simmer for 15 more minutes, until it turns into a thick stew. Stir occasionally to make sure nothing sticks to the bottom.
Prepare a batch of mashed potatoes. Spoon a generous amount of mushroom bourguignon over mashed potatoes in bowls. Enjoy!