Preheat your oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or grease well.
In a medium bowl, whisk together the gluten-free flour blend, baking soda, and salt. Set aside.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy. Beat in the egg and vanilla extract.
In a small bowl, mix the milk and sour cream/yogurt. Add the wet ingredients alternately with the dry ingredients to the butter mixture, mixing until just combined. Do not overmix.
In a separate small bowl, combine the brown sugar and 1 tablespoon of cinnamon for the swirl filling.
Prepare the swirl: Spoon about 1/3 of the batter into the prepared muffin cups. Drizzle with half of the melted butter, then sprinkle with half of the cinnamon-sugar mixture. Top with another 1/3 of the batter, the remaining butter, and the remaining cinnamon-sugar. Finish with the last of the batter. Use a toothpick to gently swirl the layers together once or twice.
Bake for 18 to 22 minutes, or until a toothpick inserted into the center comes out clean. Let the muffins cool in the tin for 5 minutes before transferring them to a wire rack to cool completely.
Prepare the glaze: Whisk together the powdered sugar, 2 tablespoons of milk, and vanilla extract until smooth. Add more milk, a teaspoon at a time, if the glaze is too thick.
Drizzle the cooled muffins generously with the glaze before serving.
Notes
Use a high-quality gluten-free all-purpose blend that contains xanthan gum for the best structure.
For a dairy-free option, substitute the butter with a solid vegan butter stick and use almond or soy milk.
Do not over-swirl the batter; too much mixing will eliminate the distinct layers.