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Place frozen rolls 2 inches apart on baking sheet lined with wax paper.
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Let rise for 1 to 1 1/2 hours or until nearly double in size.
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In a stand mixer (or using a hand-held mixer) beat cream cheese on medium-high speed until smooth.
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Add sour cream and milk; beat until combined. Remove bowl from mixer.
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Fold in 4 ounces of parmesan cheese and 4 ounces of asiago cheese by hand.
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Stir in finely chopped artichokes, finely chopped spinach, and garlic.
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Transfer artichoke mixture to a 12-inch skillet that has been buttered or sprayed with non-stick spray, spreading evenly.
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Bake for about 20 minutes or until dip is just slightly browned around edges. Remove skillet from oven.
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Arrange rolls with sides touching on top of hot dip (rolls will fit snugly and cover entire surface). (Be careful to not deflate rolls as you transfer to skillet)
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Bake for 15 to 20 minutes more or until rolls are golden and dip is hot.
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Remove from oven and sprinkle remaining 2 ounces of parmesan cheese over bread and lightly brush roll tops with melted butter.