Preheat the slow cooker on high.
Heat two tablespoons of olive oil in a large skillet. Add mushrooms and cook on high heat for about ten minutes, stirring occasionally, until any liquid is evaporated and mushrooms are browned. Add garlic, rosemary, and crushed red pepper flakes, and cook until fragrant, about one minute. Add spinach and cook until wilted, about one minute. Season with salt and pepper and remove from heat to cool slightly.
In a bowl, combine ricotta, basil, ¾ of the mozzarella, and ½ teaspoon each of salt and pepper. Fold in the mushrooms and spinach.
Spoon one cup of the sauce into the slow cooker. Arrange three lasagna noodles over the sauce, breaking them to fit. Spread ½ of the ricotta over noodles and top with one cup of the sauce. Repeat this pattern until all the sauce has been used.
Place a clean kitchen towel between the lid and the slow cooker to catch condensation. Cook on high heat for three hours, until the noodles are tender and the sauce is absorbed.
Sprinkle the remaining mozzarella on top, cover, and cook for about fifteen minutes until melted.