Preheat oven to 350°F. Grease a bundt pan thoroughly.
In a medium bowl, whisk the flour, baking powder, and salt together. Set aside.
2 ¾ cups (407g) gluten free flour blend, 2 teaspoons baking powder, ½ teaspoon salt
Using a hand mixer or a stand mixer fitted with the paddle attachment, cream butter with sugar until smooth. Add yogurt and vanilla and mix well.
1 cup (226g) unsalted butter, 1 ¾ cups (350g) granulated sugar, 1 cup (225g) Greek yogurt, 2 teaspoons vanilla extract
Add the dry ingredients to the wet ingredients and mix on low speed until combined. Add the milk and mix to combine.
½ cup (120ml) whole milk
In a separate bowl, mix together the brown sugar and cinnamon. Pour half of the cake batter into prepared pan, then sprinkle half of the cinnamon sugar mixture over it. Finish with the remaining cake batter, then top with the remaining cinnamon sugar.
¼ cup brown sugar, 1 tablespoon cinnamon
Bake for 50-55 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool for about 30 minutes in pan before inverting onto a plate.
To make the glaze:
Mix the powdered sugar with the milk until fully combined. Be sure to add the milk one tablespoon at a time as you monitor the consistency. If needed, add more milk to help thin out the glaze.