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Step 1
Preheat the oven to 400 degrees F. Pull the leaves off the thyme stems. Discard the stems and roughly chop the leaves.
Step 2
Place the cream and cornstarch in a small bowl or pot. Whisk well. Add the butter, garlic, thyme, 1 1/4 teaspoon salt, and 1/2 teaspoon pepper. Heat over the stovetop, or in the microwave, just until the butter melts. Then turn off the heat and whisk again.
Step 3
Peel and slice each sweet potato one by one. Slice the potatoes into very thin rounds, 1/8-inch thick. Arrange each potato in a 9x13-inch baking dish, fanning it out in a pretty pattern.
Step 4
Before peeling and slicing the next sweet potato, pour a little of the cream mixture over the potato slices in the pan, so it does not brown while you work on the other potatoes.
Step 5
Repeat until all the sweet potatoes are sliced and arranged prettily in the baking dish. Then pour the remaining cream mixture over the top.
Step 6
Bake for 30 minutes. Sprinkle Parmesan cheese over the sweet potatoes. Then bake another 10 minutes until the cheese is golden. Serve warm.