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Using a julienne peeler, slice the zucchini lengthwise into ribbons. Put the ribbons in a bowl and sprinkle with olive oil. Set aside to marinate and soften.
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Seed and chop the tomatoes finely. Chop the mushrooms.
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Heat a little olive oil in a skillet over medium-high heat. Add the mushrooms and cook until they are lightly browned. Season with salt and pepper.
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Stir together the cream and grated cheese in a saucepan. Bring just to a simmer over medium heat and cook a few minutes until you obtain a thick sauce. Season with salt and pepper.
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Reserve some tomatoes and mushrooms for garnish.
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Gently fold the vegetables, including the zoodles, into the cheese sauce, and garnish with the reserved tomatoes and mushrooms.
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Finish with the Parmesan cheese shavings.