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Preheat the oven to 375°F with a rack in the center. Grease an 8" square pan. Sprinkle about 2 tablespoons (18g) of the sesame seeds in an even layer across the bottom of the pan.
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In a large bowl, whisk together the flour, baking powder, baking soda, salt, and black pepper. Grate the cheese and the butter on the large holes of a box grater. Add the cheese, butter, and scallions to the dry ingredients, toss to coat, and place the bowl in the refrigerator while you prepare the rest of the ingredients.
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In a liquid measuring cup, whisk together the kimchi liquid, buttermilk, and egg until well combined. (If you are not able to get 1/4 cup kimchi liquid from straining and pressing the solids, add enough buttermilk to reach 1 1/4 cups or 283g total liquid.) Set aside.
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Add the chopped kimchi to the dry ingredients, tossing to combine.
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Pour the buttermilk mixture into the dry ingredients and stir with a fork or flexible spatula just until everything is evenly moistened.
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Transfer the batter to the prepared pan and smooth out the top. Sprinkle evenly with the remaining 2 tablespoons (18g) sesame seeds.
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Bake the kimchi cheddar bread for 38 to 45 minutes, until a toothpick or paring knife comes out clean and the temperature in the center of the bread registers at least 200°F on a digital thermometer.
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Let the kimchi cheddar bread cool in the pan for 10 minutes before transferring to a wire rack. Let it cool for another 10 minutes before slicing.
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Storage information: Store airtight at room temperature for 3 days; to reheat, wrap in aluminum foil and bake at 350°F for 10 to 15 minutes, until warmed through.
