Step 1: Prepare Your Baking Pan

1. Preheat your oven to 350°F (175°C).
2. Grease a 9×13-inch baking pan or two 9-inch round cake pans with butter or non-stick spray. Lightly dust with flour and set aside.

Step 2: Mix Dry Ingredients

1. In a medium bowl, whisk together all-purpose flour, baking powder, and salt. Set this mixture aside for later.

Step 3: Cream Butter and Sugar

1. In a large mixing bowl, use an electric mixer to beat the butter on medium speed until creamy and smooth.
2. Gradually add the sugar and continue beating for about 3-4 minutes or until the mixture becomes light and fluffy. This step is key to creating the tender crumb of the cake.

Step 4: Add Eggs and Vanilla

1. Add the eggs one at a time, beating well after each addition to ensure they are fully incorporated.
2. Add the vanilla extract and beat until combined. The batter should look smooth and creamy.

Step 5: Alternate Adding Flour and Milk

1. With the mixer on low speed, add one-third of the flour mixture to the batter and mix just until incorporated.
2. Follow by adding half of the milk, mixing until just combined.
3. Repeat with another third of the flour, the remaining milk, and then the last third of the flour, mixing after each addition until smooth. Avoid overmixing, as it can make the cake dense.

Step 6: Bake the Cake

1. Pour the batter into the prepared baking pan(s), smoothing the top with a spatula.
2. Bake in the preheated oven for 30-35 minutes (for a 9×13-inch pan) or 25-30 minutes (for 9-inch rounds), or until a toothpick inserted into the center comes out clean.
3. Remove from the oven and let the cake cool in the pan for about 10 minutes. Then transfer it to a wire rack to cool completely.

Step 7: Make the Vanilla Bean Glaze

1. In a medium bowl, whisk together the powdered sugar, milk, vanilla bean seeds (or vanilla bean paste), and a pinch of salt.
2. Adjust the glaze by adding a bit more milk if you prefer a thinner consistency or more powdered sugar for a thicker glaze.

Step 8: Glaze the Cake

1. Once the cake has completely cooled, pour the glaze over the top, spreading it with a spatula for even coverage. The glaze will set slightly after a few minutes, forming a light crust with a beautifully glossy finish.