Using a mixer, combine the butter and sugar. Mix well. Add all but ¼ cup of the milk, the egg, oil, and vanilla.
Combine the dry ingredients and add to the wet mixture. (If you don't use instant yeast, you should add it to the milk.) Beat on high until well mixed with no lumps. The dough will be soft. Add remaining milk if dough is dry.
Lay out a pastry mat or piece of plastic wrap and sprinkle it with sugar. Lay half of the dough on top and cover it with another piece of plastic wrap. Use a rolling pin to roll the dough into a 13½ inch square. Lift the top piece of plastic wrap often and reposition if necessary. You can spray the wrap with cooking spray if the dough is sticking.
Combine the filling ingredients. Remove the top layer of plastic wrap. Spread half the filling on the dough leaving a margin at one side. As you roll the dough, the filling with get shifted. The margin keeps it from being pushed all the way out at the end.
Roll the dough by lifting up the plastic wrap. Once you get the roll started, it will roll on its own. Once rolled, smooth out the edge. If you want nice clean end pieces, cut a little off each end. I leave them as is.
Cut the roll into 8 slices. I cut the roll in half, then cut each half in half, then cut the quarters in half. Use a sharp knife. I find it helps to spray it with cooking spray.
Place the rolls in a glass pie dish, using a second pie dish for the next roll, or put all of them in a 9 x 13 pan (and bake a few minutes longer).
Repeat rolling instructions for second half of the dough and bake the rolls at 375 degrees for 20 minutes.
Combine the glaze ingredients. Add milk a teaspoon at a time until the glaze is the right consistency. You can adjust the amount of glaze to your taste. Drizzle the glaze over the warm rolls and serve.
Recipe by Gluten-Free Homemaker at http://glutenfreehomemaker.com/cinnamon-roll-update/