Whisk together flour, baking powder, and salt in a medium bowl until evenly combined; set aside. Whisk together milk, ginger, and vanilla in a second small bowl until evenly combined.
Combine butter and sugar in a the bowl of a stand mixer fitted with a paddle attachment and beat on medium speed until mixture resembles wet sand and is light, about 3 minutes. Add eggs one at a time until incorporated and mixture is smooth. Scrape down mixer and sides of bowl. Reduce mixer to low, add 1/3 flour mixture and whisk until just moistened through. Whisk in 1/2 milk mixture and whisk until just moistened. Repeat until all ingredients are added, ending with flour. Transfer batter to prepared Bundt pan and smooth out so batter is even.
Bake until cake is set, golden brown, and a cake tester inserted in middle comes out clean, about 50 minutes. Transfer to a rack, let cool 10 minutes, then invert onto a wire rack, remove from pan, and let cool completely.