1. Dissolve 1 tablespoon sugar and yeast in warm milk in a small bowl; let stand 5 minutes.
2. Weigh or lightly spoon brown rice flour, potato starch, tapioca flour, and cornstarch into dry measuring cups; level with a knife. Combine brown rice flour, potato starch, tapioca flour, cornstarch, xanthan gum, salt, and 1 tablespoon sugar, stirring with a whisk. Add yeast mixture, butter, oil, and egg; beat with a mixer at medium speed until blended. Add cranberries; gently stir to combine.
3. Turn dough out onto a well-floured surface; knead gently 5 to 6 times. Roll dough to a 1/2-inch thickness; cut with a 2 1/2-inch biscuit cutter into 14 muffins. Place on a baking sheet lined with parchment paper and sprinkled with 1/2 tablespoon cornmeal. Sprinkle tops of muffins with 1/2 tablespoon cornmeal. Let rise in a warm place (85°), free from drafts, 1 hour.
4. Heat a griddle or large nonstick skillet over medium-low heat. Cook muffins 6 minutes on each side or until lightly browned. Cool completely on a wire rack.