Preheat the oven to 350°F (175°C). Grease and flour a bundt pan.

In a small bowl, mix together the brown sugar and cinnamon for the swirl.

In a large mixing bowl, cream the softened butter and granulated sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition.

Stir in the buttermilk and vanilla extract.

In another bowl, whisk together the flour, baking powder, baking soda, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Pour half of the batter into the prepared bundt pan.

Sprinkle half of the cinnamon-sugar mixture over the batter.

Pour the remaining batter on top, followed by the rest of the cinnamon-sugar mixture.

Use a knife to gently swirl the cinnamon mixture into the batter.

Bake in the preheated oven for 45-50 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cake to cool in the pan for 10 minutes before inverting onto a cooling rack.

In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth.

Drizzle the glaze over the cooled bundt cake.