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Heat a large pot over medium heat. Add olive oil, garlic, onion, and mushrooms. Cook, stirring occasionally, until onions and mushrooms have softened, 4-5 minutes.
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Add marinara, tomatoes, tomato paste, vinegar, sugar, basil, salt, oregano, pepper, bay leaf, broth. Bring to a boil over high heat, then reduce heat to low and simmer.
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Add lasagna noodles and cook, stirring often, until softened, about 15 minutes.
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Remove from heat and stir in the heavy cream and spinach until wilted, 2-3 minutes.
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Divide between bowls and top with a dollop of ricotta and a sprinkle of mozzarella.