Preheat oven to 325°.
In a mixing bowl, whisk or sift together the flour, baking powder and salt. Set aside.
In the bowl of a stand mixer, beat the butter on medium speed until creamy. Gradually add the sugar and beat until fluffy. Add the eggs, one at a time, mixing after each egg until just blended.
Pour ⅓ of the flour mixture into the butter, sugar and eggs. Mix until just incorporated. Pour in ½ of the sweetened condensed milk and mix until just combined. Repeat the flour and condensed milk steps one more time, ending with the last ⅓ of the flour mixture, making sure to mix until just incorporated.
Add in 2 teaspoons key lime zest, 1 teaspoon vanilla and ¼ cup key lime juice. Mix again until combined.
Pour the batter into a well greased bundt pan. Bake at 325° for 1 hour and 15 minutes to 1 hour and 30 minutes. Check for doneness with wooden skewers inserted into center of cake, making sure they come out clean.
Set right-side up on a wire rack and cool for 15-20 minutes. Remove from pan and continue to cool on wire rack.
Drizzle or brush glaze over top and sides of the cake. Continue to cool and let the glaze set up before cutting, which is about an hour.
