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Preheat oven to 400°F
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Prepare traditional muffin tins by coating lightly with a cooking spray, or set a silicone muffin tin aside.
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In a medium bowl, whisk eggs; combine with the wet ingredients of sour cream, butter and milk. Stir to incorporate.
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In a large bowl, combine the dry ingredients of flour, cornmeal, baking powder, baking soda, salt, thyme and sugar; stir to incorporate and make a well in the center of the mixture.
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Pour wet ingredients into the well of the dry ingredients and gently fold to mix; stir until just blended.
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Spoon batter into muffin tins about 2/3 of the way full. Bake for about 25 minutes, or until the tops are lightly browned.
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Check the doneness by inserting a toothpick in the center of one of the muffins; it should come out clean.
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Just before the muffins are done, add a small amount of honey in a saucepan and heat.
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Lightly brush the tops of each muffin right out of the oven and still hot, with a little of the honey; the heated muffins will absorb some of the honey.