1cup (2 sticks)unsalted butter,at room temperature
6ouncescream cheese,at room temperature
4largeeggs,at room temperature
1largeegg yolk,at room temperature
2½cupsroom temperature blueberries,rinsed and dried
2tablespoonsfreshly squeezed lime juice(more, as needed)
Preheat oven to 350°F. Butter and flour a 12-cup bundt pan (or use baking spray).
PREPARE THE CAKE:
In a medium bowl, whisk together the flour, baking powder and salt.
In a small bowl, combine the sugar and lime zest; use a wooden spoon to press the lime zest into the sugar and incorporate to make a lime-scented sugar.
In a large bowl, use an electric mixer to combine the butter and cream cheese on medium speed until smooth, about 1 minute. Add the lime-sugar and beat on medium speed until light and fluffy, 1 to 2 minutes. Add the whole eggs one at a time, mixing well after each addition (scrape the bowl, as needed). Beat in the egg yolk. Reduce the mixer speed to low and slowly add the flour mixture (scrape the bowl, as needed). Beat at medium speed until the batter is smooth and light (about 20 more seconds). Using a rubber spatula, gently fold in the blueberries.
Scoop the batter evenly into the prepared pan, spreading it with the rubber spatula. Tap the pan lightly against the counter to eliminate any air pockets. Bake until a wooden skewer inserted into the center comes out clean, 50 to 55 minutes. Set the pan on a wire rack to cool for at least 10 minutes and then invert onto the rack, remove the pan, and let cool completely.
GLAZE THE CAKE:
In a small bowl, whisk together the powdered sugar and lime juice until smooth. The glaze should be thin enough to pour, but thick enough to stick to the cake and not run completely down the sides. If too thin, add more powdered sugar. If too thick, add more lime juice. Put a baking sheet under the rack to catch drips; drizzle the glaze over the top and sides of the cake. Let glaze set fully before transferring to a cake plate to serve.