Heat the oven to 325°F (160°C). Butter and flour a 10-inch tube pan or two 9-by-5-inch loaf pans, tapping out any excess flour.
In a medium bowl, stir together the flour, baking powder, and salt with a fork. In a small bowl, stir the vanilla into the milk.
In a large bowl, beat the butter with an electric mixer on high speed until light and fluffy.
Add the brown sugar in 3 additions, mixing well after each addition, and then add the granulated sugar all at once, beating well after each addition. Add the eggs, 1 at a time, beating well after each addition. Add half the flour and then half the milk, beating at low speed just until the flour or milk disappears into the batter. Add the rest of the flour and then the remaining milk in the same way.
Quickly scrape the batter into the prepared pan and bake for 1 hour and 10 minutes (55 to 60 minutes for loaf pans), or until the cake is nicely browned at the edges, springs back when touched lightly at the center, and a wooden skewer inserted in the center comes out clean.
Cool the cake in the pan on a wire rack or a folded kitchen towel for 20 to 30 minutes.
Use a table knife to loosen the cake from the pan and turn it out onto a wire rack or a plate, top side up, to cool completely.