Hydrate the Porcini Mushrooms: In a medium bowl, pour hot water over the porcini mushrooms, weighing the mushrooms down with a smaller bowl so they stay submerged. Soak for 10 minutes. Strain the porcini mushrooms through a fine mesh strainer lined with a coffee filter or cheesecloth. Reserve ½ cup of the mushroom broth for the bolognese. Rinse the porcini mushrooms under running water, then squeeze out excess water. Set aside.
Chop the Veggies: In a food processor fitted with the S blade, working in four batches, pulse the crimini mushrooms 5-6 times to a small dice about ¼-½ inch in size, transferring each batch to a large bowl. Set aside. To the empty food processor, add the carrot, celery and onion. Pulse about 10-13 times to finely chop the vegetables. Transfer the veggies to the large bowl with the crimini mushrooms. To the empty food processor, add the porcini mushrooms and pulse 7-8 times or until finely chopped. Transfer the porcini mushrooms to the large bowl with the crimini mushrooms and veggies. To the empty food processor, add the canned tomatoes and all their juices. Pulse 7-8 times, until finely chopped. Some chunks are okay. Set aside.
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 incorporate.
Transfer to pasta bowls and serve with grated Parmesan, torn fresh basil or chopped parsley.
