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Heat the oil and 1 tablespoon of butter in a large skillet over medium high until shimmering. Add the onion with a pinch of salt. Cook, stirring, until the onions are translucent and starting to get golden, about 10 minutes.
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Add the thyme and garlic and mix. Cook for another 1-2 minutes.
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Add the mushrooms with another pinch of salt. Cook, stirring, until the mushrooms have released their water and have shrunk a bit, 5-8 minutes.
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Add the wine and stir, cooking until the moisture has evaporated.
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Add the cream and asparagus and toss. Cook until the sauce has thickened and the asparagus is heated through.
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Add salt and freshly ground black pepper to taste. Add the remaining 2 tablespoons of butter, as well as the cooked pasta, and toss. Serve immediately.