Preheat the oven to 400 degrees F and line a rimmed baking sheet with parchment paper.
Cut the spaghetti squash in half from top to bottom. Scoop out and discard the seeds. Place the squash on the prepared baking sheet cut-side up. Drizzle each half with about 1 1/2 teaspoons olive oil and season with a generous pinch of salt and black pepper. Turn the squash cut-side down and bake until a fork easily pulls the “spaghetti” strands away from the squash, about 40 minutes.
In the meantime, start the sauce. Heat a Dutch oven or large pot over medium heat and add enough olive oil to coat the base of the pot, about 2 tablespoons. Add the garlic, carrot, celery and onion to a food processor fitted with the blade attachment. Pulse the vegetables until finely chopped. Add the vegetables to the heated pot and season with 1/2 teaspoon each salt and black pepper. Sauté the vegetables, stirring occasionally, until they soften, about 5 minutes. Re-attach the food processor bowl and add the mushrooms and zucchini. Pulse the vegetables until finely chopped but still with some texture. Add them to the pot with the other vegetables. Season with another 1/2 teaspoon each salt and pepper. Cook, stirring occasionally, until the vegetables are soft and their natural liquid has mostly evaporated, 7 to 10 minutes.
Add the milk and cook, stirring occasionally, until the milk is mostly evaporated, about 5 minutes. Next, add the red wine and cook, stirring occasionally, until the wine is mostly evaporated, about 7 minutes.
Add the crushed tomatoes, basil, red pepper flakes, cheese rind and 1/2 teaspoon salt. Bring the sauce up to a low boil, then reduce the heat to low, cover the pot and simmer for 15 minutes. Remove the lid and let the sauce simmer for an additional 15 minutes. Remove the cheese rind and discard. Season the sauce to taste.
To serve, add spaghetti squash to individual bowls and top with a big ladle of sauce, freshly grated Parmesan and torn basil.