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Bring a medium pot of water to a boil.
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Cut each peeled sweet potato into 6 large chunks. Drop the potatoes into the boiling water. Boil for five minutes, remove from heat, drain, and then leave the potatoes in the pot covered.
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Preheat the oven to 375 degrees F.
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In a small saucepan, melt the butter over medium/low heat. Once the butter is melted, add in the onion and thyme. Sauté for two minutes.
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Whisk in the flour until it is absorbed by the butter, one minute. Whisk in the Greek yogurt until combined. Pour in the milk slowly while whisking. Whisk for a minute or two until combined.
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Turn heat down to low. Add ¾ cup cheese, salt, and pepper. Mix to combine until the cheese melts and the sauce is smooth yet thick. Once combined, shut heat off. Taste sauce and adjust salt and pepper to your taste.
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Add kale and sweet potatoes to a large casserole dish. Pour in the cheese sauce and mix to combine. Top with remaining ¼ cup shredded cheese. Bake dish in oven for 30-35 minutes. Let dish cool for 5-10 minutes before serving to allow the sauce time to set up. Store in the refrigerator in an airtight container for up to three days. Reheat in the microwave or in the oven.