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In a small saucepan, heat milk and 3 tablespoons of butter to 110 degrees. Remove from heat. Sprinkle yeast over the top of the milk mixture and allow to set for 10 minutes until bubbles begin to form. Add salt and 1 tablespoon of sugar and stir.
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Add yeast mixture to the bowl of a stand mixer fitted with the dough hook attachment. Turn mixer to low and add flour 1/2 cup at a time until the dough comes together. Knead for 3 minutes. Dough will be sticky.
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Transfer dough to a well oiled bowl, cover and place in a warm spot to rise for one hour or until doubled in size.
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On a floured surface, roll dough into a thin rectangle. Brush with 3 tablespoons melted butter.
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In a medium bowl combine remaining 1/4 cup sugar, cinnamon, and strawberries. Spread berry mixture evenly over the top of the dough.
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Starting at one end, tightly roll up the dough lengthwise. Using a serrated knife, cut the dough into 1.5 - 2 inch sections and place in a greased 8x8 square pan (you should have about 10 rolls). Brush with remaining 2 tablespoons melted butter. Cover with plastic wrap. Set on top of the oven to let rise again for 30 minutes while you preheat oven to 350 degrees.
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Bake for 30-35 minutes until golden brown.
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Meanwhile, using a mixer, beat cream cheese until light and fluffy. Gradually add one cup of powdered sugar. Beat until well combined. Carefully add champagne and remaining cup of powdered sugar. If mixture seems too thin, add more powdered sugar until desired consistency is reached.
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Spread frosting over warm rolls and serve immediately