Make the dough. Separate ½ cup of flour and set aside. In a large bowl, stir together the remaining flour, the sugar, salt and yeast together until evenly dispersed. Set aside.
In a heatproof bowl, heat the water, half-and-half and butter together in the microwave until the butter is melted and the mixture is hot to touch. Stir to combine, then slowly pour the butter mixture into the flour mixture. Add the egg and only enough of the reserved ½ cup flour to make a soft dough. (I only needed ¼ cup.) Dough will be ready when it has an elastic, stretchy consistency and it gently pulls away from the side of the bowl.
On a lightly floured surface, knead the dough for about 3 to 4 minutes. Grease a bowl with non-stick spray and place the dough in the bowl. Allow to rest for about 10 minutes. Preheat the oven to 200°F (93°C).
Make the filling. In a clean bowl, mix together the cinnamon, sugar and baking spice. After 10 minutes, use a lightly floured rolling pin to roll the dough into a 14x8-inch rectangle. Use the back of a spoon to spread the softened butter on top, then sprinkle the cinnamon sugar all over the dough. Tightly roll up the dough. (Cinnamon may spill out the edges.) Cut the roll into 12 even pieces and place in a lightly greased 9-inch round pan.
Turn off the oven. Loosely cover the rolls with a sheet of aluminum foil. Allow them to rise in the warm oven for 60-90 minutes.
After the rolls have doubled in size, preheat the oven to 375°F (190°C). Bake for 25 to 30 minutes, until lightly browned. Covered with aluminum foil after 15 minutes to avoid heavy browning.
Make the glaze. While the rolls are cooking, make the glaze. In a saucepan over medium heat, melt the butter and heat until golden brown, stirring often, about 10 minutes. The butter will bubble and froth as it cooks. When the butter turns a medium golden brown, transfer to a large, heat-proof bowl.
Add sugar and 2 tablespoons milk to the brown butter and stir until smooth. If glaze is too thick, add more milk. If it is too runny, stir in a teaspoon of confectioner's sugar. Use immediately to top cinnamon rolls with glaze.
Notes
The rolls are best eaten warm on the same day, but they will keep fresh and soft in an airtight container at room temperature or in the refrigerator for 5 days. Glaze the rolls immediately before serving.You may make the dough ahead of time the night before, through step 4. Form the dough into a ball and cover with plastic wrap. Let it rise in the refrigerator overnight. The next morning, remove from the refrigerator and let rise some more, about 1 hour.