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In a small sauce pan, heat 3/4 cup milk almost to a boil over medium heat. Do not boil. Set aside to cool for 10 minutes.
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Sprinkle yeast over water. Set aside to soften for 5 minutes.
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In a large bowl combine sourdough starter, cooled milk, softened yeast mixture, butter or margarine, sugar and salt. Stir in enough flour to make a soft dough.
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Turn out onto a lightly floured surface. Clean and grease bowl, set aside.
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Knead dough 5 to 8 minutes or until smooth and elastic. Add more flour if necessary.
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Place dough in greased bowl, turning to grease all side. Cover with with plastic wrap. Place in refrigerator 2 hours or overnight.
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Grease a large baking sheet. Set aside. Punch down dough. Turn out onto a lightly floured surface. Divide dough into 24 to 30 equal pieces.
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Gently roll each piece between your hands to a 15-inch rope. On prepared baking sheet loosely coil each rope, tucking the end of the rope under coil. Leave 2 inches between coiled roll.
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Cover with a cloth and set in a warm place free from drafts. Let rise 1 to 2 hours or until doubled in size.
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Preheat oven to 400 Degrees. Press the center of each roll with your fingers until you touch the baking sheet. Making indentations about an 1inch wide. Spoon cherry pie filling into each indentation.
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Bake in preheated oven 12 to 15 minutes or golden brown. Remove baking sheet. Cool on rack.
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In a small bowl, combine powdered sugar, vanilla and 1 tablespoon milk. Beat until smooth. Using a spoon drizzle over the rolls.