Dissolve yeast in warm water. Beat in sugar, salt, oil, egg and 1 cup flour until smooth. Stir in enough remaining flour to form a soft dough. Turn onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and refrigerate 4 hours.
Crumble mincemeat into a small saucepan; add cider. Bring to a boil; cook and stir for 1 minute. Remove from the heat. Cool completely. Combine brown sugar and cinnamon; set aside.
Punch dough down. Turn onto a floured surface. Roll into a 16-in. x 12-in. rectangle. Spread filling to within 1/2 in. of edges; sprinkle with brown sugar mixture. Dot with butter.
Roll up jelly-roll style, starting with a long side; pinch seam to seal. Cut into 16 rolls. Place cut side up in two greased 9-in. round baking pans. Cover and let rise until doubled, about 1 hour.
Bake at 350° for 25-30 minutes or until golden brown. Combine glaze ingredients; drizzle over warm rolls.