Return the heat on the mushrooms to medium-high. Add the mirepoix back to the pot and stir to combine. Add two tablespoons tomato paste and use your spoon to coat the vegetables with the paste.
Once the paste begins to deepen in color (about 2 minutes), pour in the white wine and scrape up any browned bits stuck to the bottom of the pot. Pour in the vegetable stock, whole-peeled tomatoes, and crushed tomatoes. Taste and season with a touch of salt, pepper, sugar, and crushed red pepper. Do not over-season at this point as the ragù will cook down for a bit.
Turn the heat to low and cook, partially covered, for 45 minutes to 1 hour, stirring occasionally. As the ragù cooks, use your spoon to lightly mash the whole-peeled tomatoes. After 45 minutes, taste the sauce and season to your preferences.