Preheat oven to 350°F. Grease a bundt pan thoroughly.
In a medium bowl, whisk the flour, baking powder, and salt together. Set aside.
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.
Add the dry ingredients to the wet ingredients and mix on low speed until combined. Add the milk and mix to combine.
In a separate bowl, mix together the brown sugar and cinnamon. Pour half of the cake batter into prepared pan, then sprinkle the cinnamon sugar mixture over it. Finish with the remaining cake batter.
Bake for 45-50 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool for about 5 minutes in pan before inverting onto a plate.
To make the glaze:
Mix the powdered sugar with the heavy cream until fully combined. Be sure to add the cream one tablespoon at a time as you monitor the consistency. If needed, add more cream to help thin out the glaze.
If you prefer a thinner glaze, feel free to use milk instead of heavy cream. You can also add a splash of milk to the powdered sugar + heavy cream to thin it out if desired.