Pour balsamic vinegar over prunes in a small bowl and set them aside to soak.

Warm the oil in a large sauté pan over medium heat. Add the onion and carrots, season with salt to taste, and sauté for 10 minutes, until the onion is translucent and slightly golden.

Add the mushrooms to the onions and sauté until all their juices evaporate, 8 to 10 minutes. Add the garlic, chili, thyme, rosemary, and black pepper to taste, and cook for 2 to 3 more minutes.

Increase the heat to medium high. Add the balsamic vinegar from the bowl with the prunes, along with the lemon juice, tomato paste, and tamari; toss to combine. Add the prunes to the pan. Cook a few more minutes, stirring often, until the liquid is almost completely evaporated.

Add the tomatoes to the pan and reduce the heat to a slow simmer. Cover and cook for 30 to 40 minutes, stirring occasionally, until thickened. Taste for salt and pepper and adjust if necessary. Remove the pan from the heat.

While the sauce is cooking, bring a large pot of well-salted water to a boil. Add the spaghetti and cook it to al dente according to the directions on the package. Drain the pasta, reserving ¼ cup of the cooking water.

Return the pasta to the pot, add the mushroom Bolognese and reserved pasta cooking water, and toss to combine. Divide the pasta among individual bowls and serve immediately, garnished with herbs and grated Parmesan, if using.