Stir the brown sugar and cinnamon together in a small bowl until combined; set aside.

Beat the butter and granulated sugar on medium speed until pale and fluffy, about 3 minutes.

Add the eggs one at a time, then mix in the vanilla. Whisk the flour, baking powder, baking soda, and salt in a separate bowl. With the mixer on low, add the flour mixture and buttermilk alternately in three and two additions, starting and ending with flour, mixing just until combined.

Grease and flour a 10- to 12-cup Bundt pan. Spread half the batter in the pan, sprinkle the cinnamon sugar evenly over it, top with remaining batter, and smooth the surface. Swirl once with a butter knife in a figure-eight motion.

Preheat the oven to 350°F (175°C) and bake the cake on the lower rack for 50 to 60 minutes, until a skewer comes out with a few moist crumbs. Cool in the pan on a wire rack for 10 minutes.

Run a spatula around the edges, invert onto a serving plate, and slice warm or at room temperature.