Move an oven rack to the center position and preheat the oven to 350°F (175°C). Generously spray the inside of a bundt pan with nonstick baking spray with flour, reaching every ridge, the center tube, and the top rim.
Whisk together the flour, baking powder, and salt in a medium bowl for about 30 seconds until evenly combined. Set aside.
Beat the softened butter and granulated sugar on medium-high speed for 3 to 4 minutes until pale, light, and fluffy, scraping down the bowl once or twice.
Reduce speed to medium and add the eggs one at a time, beating about 30 seconds after each. Add the vanilla and mix for another 20 seconds, then scrape the bowl.
On low speed, alternate adding the flour mixture and milk in three additions, beginning and ending with flour. Mix just until no dry streaks remain, then gently fold the batter with a spatula.
Spoon the batter into the prepared pan in even dollops and smooth the top. Lift the pan a few inches and tap it firmly on the counter 4 or 5 times to release air bubbles.
Bake on the center rack for 50 to 60 minutes, without opening the oven during the first 40 minutes. The cake is done when a tester comes out clean or the center reads 205°F to 210°F (96°C to 99°C).
Let the cake rest in the pan for 15 minutes, then invert it onto a wire cooling rack and lift the pan slowly. Cool completely, about 1 hour, before glazing.
Whisk the powdered sugar, 2 tablespoons milk, vanilla, and a pinch of salt until smooth, adding more milk 1 teaspoon at a time until the glaze falls off the whisk in a thick ribbon. Spoon over the cooled cake and let set for 15 to 20 minutes.