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Combine ¾ cup flour, undissolved yeast, sugar, salt, and garlic powder in a large bowl. Heat milk, water and butter until very warm (120° to 130°F). Add to flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add ¼ cup flour; beat 2 minutes at high speed. Stir in enough remaining flour to make soft dough; add cheddar. Knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover; let rest 10 minutes.
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Divide dough into 12 equal pieces. Roll each piece to a 12-inch rope. Tie loose knot in center and tuck ends under. Place on greased baking sheet.Cover; let rise in warm, draft-free place until doubled in size, about 30 minutes.
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Bake in preheated 375°F oven for 20 minutes or until done.
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A couple minutes before the rolls are done, melt the 1 tablespoon butter and stir in garlic powder. Brush rolls with this immediately after you pull them out of the oven.
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Serve warm.