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Heat the olive oil in a large deep dish pan or dutch oven. On low-medium heat, cook the onions until soft. (This will take about 8-10 minutes).
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Add the mushrooms (along with the salt and pepper) and cook until most of the liquid in the mushrooms is evaporated and the mushrooms reduce in size. (This will take about 6 to 8 minutes, depending on how much liquid is in the mushrooms).
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Stir in the ground sausage. Stir and break down the sausage with a wooden spoon. Cook until non longer pink. (About 5 to 6 minutes).
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Stir in the diced garlic and cook for an additional minute or two.
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Raise heat to medium. Pour in the white wine and cook until the wine evaporates. (About 5 to 6 minutes).
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Stir in the heavy cream and cook until the liquid reduces. (About 5 to 6 more minutes).
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Turn the heat off. Stir in the Ricotta, Parmesan, and Pecorino Romano.