In a mixing bowl, whisk together gluten-free flour, yeast, granulated sugar, and salt.
Add warm milk, melted butter, vanilla extract, and egg, mixing until a soft dough forms.
Let the dough rise for 1 hour in a warm place.
Roll out the dough into a rectangle, brush with melted butter, and sprinkle brown sugar and cinnamon evenly.
Cut into strips, stack them, then slice into squares and arrange in a greased loaf pan.
Let it rise for another 30 minutes.
Bake at 350°F (175°C) for 30-35 minutes until golden brown.
Cool slightly before pulling apart and serving.