In a large 7 quart Dutch oven, add the olive oil and heat on medium until it shimmers. Add the vegetable and mushroom mixture all at once and stir to coat the veggies in oil. The pot will be full. Place the lid on the pot and cook for 5 minutes on medium heat. The veggies will release their liquid and begin to cook down. Remove the lid and continue cooking on medium to medium-high heat, stirring occasionally until all the liquid evaporates, about 5-7 minutes. Some sticking is okay, and the veggies should start to brown. Stir in garlic and tomato paste. Cook, stirring for about a minute.
Pour in the wine, stir, and cook until almost all the wine has evaporated, about 2-3 minutes. Add the reserved mushroom broth, tomatoes, baking soda, tamari, salt, black pepper and red pepper flakes. The mixture will bubble up a bit from the baking soda. Bring to a simmer, then reduce heat to medium-low, cooking (without the lid) for 10-15 minutes or until the sauce thickens slightly.
Remove the bolognese from the heat and stir in the cream. Taste for salt and adjust to taste. Lid to keep warm.
Meanwhile, put a large pot of salted water on to boil and cook the pasta according to package directions. Drain. Transfer pasta to the sauce, gently stirring to incoporate.
Transfer to pasta bowls and serve with grated Parmesan, torn fresh basil or chopped parsley.
Reheat: reheat on low heat in a lidded pot. This helps retain the pasta's texture. Give it about 10-15 minutes, stirring occasionally to prevent sticking. Add a splash of cream or milk as needed. To Freeze: the sauce can be frozen (without the pasta), for up to several weeks. Cool completely, then store in a lidded container. Thaw in the refrigerator before gently reheating on stove top. I do not recommend freezing pasta generally. It breaks down and impacts the texture. If needed, serve the sauce and pasta separately.