Position a rack in the center of the oven and heat the oven to 350°F. Butter and flour a 12-cup Bundt pan.
8 oz. (1 cup) unsalted butter, 10-1/2 oz. (2-1/3 cups) all-purpose flour
Sift the flour, baking powder, and salt into a medium bowl.
1-1/2 tsps. baking powder, 1/4 tsp. plus 1/8 teaspoon table salt
Using a stand mixer fitted with the paddle attachment or a hand mixer, beat the butter and cream cheese until smooth, about 1 minute. Add the sugar and beat on medium speed until light and fluffy, about 2 minutes. With the mixer still running, add the whole eggs one at a time, then add the egg yolk, followed by the lime zest. Stop and scrape down the bowl. Reduce the mixer speed to low and slowly add the flour mixture. Scrape down the bowl again and beat just until the batter is smooth—don’t overmix. Using a rubber spatula, gently fold in the blueberries.
6 oz. cream cheese, 1-3/4 cups granulated sugar , 4 large eggs plus 1 large egg yolk, zest of one lime, 2-1/2 cups (13 oz.) room-temperature blueberries
Transfer the batter to the prepared pan and spread it evenly with the spatula. Run a knife through the batter to eliminate any air pockets. Bake until a toothpick inserted into the center comes out clean, 50 to 55 minutes. Set the pan on a wire rack and cool for 20 minutes before inverting the cake onto the rack. Let cool completely.
In a spouted measuring cup or small bowl, whisk the confectioners’ sugar and lime juice together until smooth. The glaze should be thin enough to pour; if it’s too thick, add more lime juice in small increments. Drizzle the glaze over the top and sides of the cake.
4 oz. (1 cup) confectioners' sugar, 2 tbsps. fresh lime juice, more as needed