Preheat oven to 400ºF.
Heat neutral oil in a wide pot over medium-high heat. Add half the mushrooms and cook for 8–10 minutes until they turn golden brown and crisp up around the edges. Season with salt and pepper and transfer to a bowl. Add more oil and the remaining mushrooms and cook an additional 8–10 minutes. Transfer to the bowl of mushrooms.
Add the onion to the pot and cook for 5–6 minutes until it softens. Return the mushrooms to the pot and add the garlic, dry thyme, and a big pinch of crushed red pepper.
Turn the heat to high, and as soon as the mushrooms begin sizzling hard in the pot, pour in the sweet vermouth. Stir to lift anything stuck to the bottom of the pot and bring it to a boil. Reduce heat and cook for 3–4 minutes.
Add the crushed tomatoes and tomato sauce to the pot and boil. Add a pinch of sugar if you like. Reduce heat and stir in the basil and parsley. Simmer, uncovered, for 30–40 minutes. Taste and season with salt and pepper.