Set oven to 325°F (163°C). Grease and flour a bundt or tube pan. Whisk flour, baking powder, baking soda, and salt. Set aside.
Beat softened butter and sugar until light and fluffy (3–5 minutes).
Mix in eggs one at a time, fully incorporating each. Mix buttermilk and vanilla together.
Add dry and wet ingredients alternately to butter mixture, starting and ending with dry. Mix until just combined.
Pour batter into pan and bake 60–70 minutes. Check doneness with a toothpick. Cool cake in pan 10–15 minutes, then invert onto wire rack to cool completely.
Beat cream cheese, powdered sugar, milk, and vanilla until smooth. Thin with milk if needed.
Drizzle glaze over cooled cake and let set 15–20 minutes before serving.