Pulse the cremini mushrooms in a food processor in batches until the pieces are no larger than half an inch, about 5 to 7 pulses, and transfer them to a large bowl. Pulse the carrot and onion in the empty processor until finely chopped and add them to the mushrooms. Pulse the tomatoes and their juice until chopped fine and set aside separately.

Melt the butter in a Dutch oven over medium heat. Add the processed mushrooms, carrots, onions, and the porcini mushrooms, then cover and cook until the vegetables release their liquid, about 5 minutes.

Uncover the pot, increase the heat to medium-high, and cook until the liquid has evaporated and the vegetables begin to brown, about 12 to 15 minutes.

Stir in the garlic and sugar and cook until fragrant. Add the tomato paste and cook for 1 minute until it darkens slightly. Pour in the wine and simmer until it has nearly evaporated, about 5 minutes.

Stir in the processed tomatoes, vegetable broth, soy sauce, salt, and pepper and bring to a simmer. Reduce the heat to medium-low and simmer until the sauce has thickened but is still moist, 8 to 10 minutes. Remove from the heat and stir in the cream.

Bring 4 quarts of water to a boil in a large pot while the sauce simmers. Add the pasta and salt, cooking until al dente. Reserve half a cup of the cooking water, then drain the pasta and return it to the pot.

Toss the pasta with the mushroom sauce, adjusting the consistency with the reserved cooking water as needed. Season with salt and pepper to taste and serve immediately with Parmesan.