Crack the eggs into a separate bowl. Sift the flour into a large bowl. Add the baking powder and salt and whisk the ingredients together.
Put the butter and the vanilla bean paste in the bowl of a stand mixer and with the paddle attachment beat the butter and vanilla for 30 seconds on medium speed.
With the mixer running on medium speed slowly add the sugar 1/2 cup at a time beating for 30 seconds after each addition before adding the next 1/2 cup of sugar. After adding all the sugar beat the sugar and butter together for until the mixture is creamy, about 5-6 minutes.
Scrape the bottom and sides of the bowl. Add the eggs one at a time and beat on medium speed until each egg is well incorporated.
Stop the mixer after adding the first 3 eggs and scrape the bottom of the bowl to ensure the ingredients are well mixed. Add the remaining 2 eggs one at time and scrape the down the after mixing in the last egg.
Add one-third of the dry ingredients and mix on low speed until well combined, but do not over mix. Add one-half of the whole milk and mix on medium speed until well combined. Add half of the remaining dry ingredients, then the rest of the milk. Add the remaining the dry ingredients and mix until just combined. Scrape the bottom of the bowl and mix on low speed for about 30 seconds.
Scoop the batter into the prepared bundt pan. Use an offset spatula to smooth the top of the cake so it is level. Fold a dish towel and place it on the counter. Tap the bundt pan against the counter 4 times to remove air bubbles from the batter.
Bake the cake for 45-55 minutes and rotate the cake after the frist 25 minutes. The is done when it is golden brown and a skewer inserted in the center of the cake comes out with no more than a couple of crumbs clinging to it. Another way to check it is with an instant-read thermometer. The temperature should be 202°F.