Begin by preheating your oven to 350°F (175°C).
In a microwave-safe dish, melt 2 tablespoons of butter. Once melted, use a pastry brush to generously coat your bundt pan with the melted butter, making sure to reach all the nooks and crannies. Allow the butter to cool a bit.
After the butter has cooled, sprinkle a handful of flour into the pan. Tilt and tap the pan to evenly coat it with a thin layer of flour. Invert the pan over your sink or trash can to remove any excess flour. Set the prepared Bundt pan aside.
In a medium-sized bowl, mix together the flour, baking powder, and salt. Set this dry ingredient mixture aside.
In a large mixing bowl, use an electric hand mixer or a stand mixer to cream the softened butter until it becomes creamy and smooth. Add the sugar and continue to mix for about 3-4 minutes, or until the mixture is fluffy.
Add the eggs one at a time, thoroughly mixing between each addition. After the last egg, blend in the vanilla extract until well combined.
Gradually sift in the dry flour mixture and mix at low speed until it's almost fully combined.
Pour in the milk and mix at low speed until the batter is just combined.
Scoop out approximately 500g of the batter into a separate medium bowl to make the cinnamon swirl batter. In this bowl, add the brown sugar, cinnamon, and milk. Gently fold the ingredients together until well combined.
Begin assembling the cake in your prepared bundt pan. Start by adding a few dollops of the vanilla batter and use a spatula to spread it into a thin, even layer. Continue this process, alternating between the vanilla and cinnamon swirl batters until you've used up all the batter.
Bake the bundt cake in the preheated oven for 50-55 minutes, or until a toothpick inserted into the center comes out mostly clean.
Allow the cake to cool in the pan for 20-30 minutes. To remove it from the pan, place the wire rack upside down on top of the cake, hold both the pan and rack, and flip them over, so the pan is now on top of the rack. Carefully lift the sides of the pan to release the cake. Sprinkle the Bundt cake with powdered sugar and enjoy it while it's warm or let it cool completely.