Combine yeast and 3/4 cup water in a glass measuring cup; let stand 5 minutes.
Beat yeast mixture, 1/4 cup sugar, and next 4 ingredients at low speed with an electric mixer until blended.
Turn dough out onto a well-floured surface, and knead until smooth and elastic (about 4 minutes).
Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in bulk.
Punch dough down, and divide into 12 portions. Roll each into a 3-inch circle.
Brush circles lightly with butter, reserving remaining butter.
Combine remaining 3/4 cup sugar and cinnamon; sprinkle evenly over circles. Place cranberries evenly in center of each circle, and top with a marshmallow.
Pull edges of circle to center, and pinch to seal; shape into a ball. Place, seam side down, in lightly greased muffin pans. Brush tops with reserved butter. Cover and chill 8 hours.
Remove from refrigerator, and let rise in a warm place, free from drafts, 30 minutes or until doubled in bulk.
Bake at 400° for 12 minutes or until lightly browned; cool slightly.
Stir together powdered sugar, milk, and ginger; drizzle over rolls.
Prep: 40 min.; Rise: 1 hr., 15 min.; Chill: 8 hrs.; Bake: 12 min