In a light-colored medium saucepan, melt butter over medium-high heat. Cook, stirring frequently, until butter is fragrant and a deep amber color, 8 to 10 minutes. Pour into a shallow baking dish, and let cool until solid but still soft.

Preheat oven to 325°F (170°C).

In the bowl of a stand mixer fitted with the paddle attachment, beat browned butter and brown sugar at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in vanilla.

In a medium bowl, whisk together flour, baking powder, and salt. With mixer on low speed, gradually add flour mixture to butter mixture alternately with milk, beginning and ending with flour mixture, beating just until combined after each addition.

Spray a 10-cup Bundt pan with baking spray with flour. Spoon batter into prepared pan. Tap pan on a kitchen towel-lined counter to settle batter.

Bake until a wooden pick inserted near center comes out clean, 1 hour to 1 hour and 10 minutes. Let cool in pan for 10 minutes. Invert cake onto a wire rack, and let cool completely.

Top cooled cake with Brown Sugar Glaze. Let stand until set, about 10 minutes. Store in an airtight container for up to 3 days.