Prepare the Icing: In a small bowl, mix the powdered sugar with water or dairy-free milk. Add the liquid gradually, stirring well after each addition until you get a thick, drippy consistency. Set aside.
Grease the Mug: Use a tiny dab of oil to grease a regular-sized drinking mug (about 11 to 12 oz).
Make the Dough: In a small bowl, combine the flour, baking powder, and salt. Stir in enough water (about 4 tablespoons) to form a slightly tacky but not sticky dough. Knead gently to bring it into a ball, being careful not to overwork the dough.
Roll Out the Dough: Dust a clean surface with flour and roll the dough into a long strip about 4 inches wide and ⅛ inch thick.
Add Cinnamon and Sugar: Sprinkle the brown sugar and cinnamon evenly over the dough. Fold the long edges inwards to meet in the middle, sealing in the cinnamon and sugar.
Roll and Place in Mug: Roll the dough tightly and gently place it in the greased mug. Add ½ teaspoon of water to the mug to create steam during cooking.
Microwave: Microwave uncovered on full power for about 50 seconds (adjust if needed based on your microwave’s wattage). The roll should puff up and nearly reach the top of the mug. Check for doneness using a toothpick; it should come out clean.
Add Icing: Spoon the icing over the cinnamon roll while it’s still in the mug or turn the roll out onto a plate before icing. Enjoy immediately while warm.