Make the dough. Mix the dry ingredients together in the bowl of a stand mixer fitted with a paddle attachment. Add the water, butter, apple cider vinegar, and egg and beat until the dough is smooth. It will be slightly wet and sticky. Turn the dough out into a greased bowl, cover with plastic wrap and allow to double in size. If you prefer, let the dough rise for 8 hours (or overnight) in the refrigerator.
Lightly dust a work surface with fine brown rice flour and turn your dough out. Dust the top of the dough with more flour and roll out into a 12 x 9 inch rectangle, running an offset spatula under the dough now and then to make sure it isn’t sticking to the surface. If it sticks, gently lift an edge and toss a little more flour under the dough.
Once your dough is rolled out sprinkle the top evenly with the brown sugar and spices, then drizzle the butter evenly over the sugar.
Sprinkle the remaining ingredients over the top and then roll, starting at the long edge furthest from you, using that offset spatula as necessary to help.
Using a sharp knife, cut the log in half, then cut each half in half. The cut the halved halves in half so you have 8 rolls total. They should each be about 1½ inches thick.
Grease a 9-inch round cake pan with (gluten-free) cooking spray and carefully arrange rolls in the pan. Cover with plastic wrap and let rise until double, about 1 hour at room temperature, or in the fridge overnight.
Bake at 350 degrees F for about 45 minutes, or until cooked through.
Make the glaze. Beat the butter and cream cheese together until light and fluffy. Add the powdered sugar and milk and beat until the glaze is smooth. Add additional milk, as needed, for a spreadable consistency. Smear over the top of the warm cinnamon rolls. Garnish with a rolled, candied carrot curl if you're feeling fancy.