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Cook the pasta while making the sauce. Boil a stockpot of water, when boiling add fettucine, pinch of salt, and a drizzle of olive oil. Cook for 8-10 minutes. Drain and set aside.
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Heat a medium skillet on low heat. Melt the butter in the pan and add the minced garlic.
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Measure out broth and mix cornstarch right into the cup by rubbing the whisk between your hands.
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Once the garlic is fragrant and begins to brown, pour in the broth & cornstarch mix and raise the heat to medium. Season with salt, pepper, and oregano.
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Once it starts to simmer, turn the heat off. Slowly stir in the half and half, parmesan, and Greek yogurt. Make sure the temperature is not too hot or it will curdle.
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Turn the heat back on to low, only to heat through. Toss fettucine into the sauce. Serve with fresh parsley on top.