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In a deep skillet or dutch oven, melt the butter over medium heat and then add the sliced onions. Stir occasionally while doing the next steps.
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Start water heating for your pasta. Salt the water enough that it tastes pleasant on its own.
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Meanwhile, slice or chop your mushrooms. I use an egg-slicer to make it fast but if I'm without one, I quarter the mushrooms unless they're huge. Add them to the onions as you go.
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Cook the onions and mushrooms until they've released their liquid and it's mostly evaporated, about 10 minutes. Stir frequently at this point to keep them from burning.
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Start cooking your pasta according to package directions.
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Add the flour to the onion-mushroom mix and stir until it's well-mixed. Cook for one minute, then add the milk. Cook, stirring frequently, until the mixture thickens. Reduce the heat to low.
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Add the Greek yogurt or sour cream and stir continuously until the mixture starts to bubble just a bit. Remove from heat and then season to taste with salt and pepper.
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Drain your pasta and then serve the mushroom mix on top of individual servings of pasta. Garnish with parmesan cheese and parsley.