Activate the yeast: In a small bowl, combine the warm milk, 1 teaspoon of sugar, and yeast. Let stand for 5 to 10 minutes until foamy.
In a large bowl, cream together the 1/4 cup granulated sugar and 1/2 cup softened butter until light and fluffy. Beat in the eggs one at a time.
Mix the gluten-free flour blend, salt, and baking powder in a separate bowl. Gradually add the dry ingredients to the wet ingredients, mixing until a soft, slightly sticky dough forms.
Pour the activated yeast mixture into the dough and mix until just combined. The dough will be softer than wheat dough.
Cover the bowl with plastic wrap and let the dough rise in a warm place for 60 to 90 minutes, or until it has visibly increased in volume.
Prepare the filling: In a small bowl, mix the melted butter, brown sugar, and cinnamon.
Turn the dough out onto a lightly floured surface (use extra gluten-free flour). Gently pat or roll the dough into a rectangle approximately 12×18 inches.
Spread the cinnamon-sugar mixture evenly over the dough surface, leaving a small border on one long edge.
Roll the dough tightly starting from the long edge opposite the border. Pinch the seam closed.
Cut the log into 12 equal rolls. Place the rolls cut-side up in a greased 9×13 inch baking pan.
Cover the pan loosely and let the rolls proof for a second time in a warm spot for 30 minutes. Preheat your oven to 375 degrees Fahrenheit during this time.
Bake for 20 to 25 minutes, or until the tops are lightly golden brown.
Prepare the icing while the rolls cool slightly: Whisk together the powdered sugar, milk, and vanilla extract until smooth.
Drizzle the icing over the warm rolls before serving.
Notes
If your gluten-free flour blend does not contain xanthan gum, add 1 teaspoon to the dry ingredients.
Gluten-free dough handles best when slightly sticky; avoid adding too much extra flour during rolling.
For a chewier result, let the dough rise in a slightly cooler spot for a longer period.