16tbsp(2 sticks) unsalted butter,cool room temperature
2cups(14 ounces) granulated sugar
2tbspfresh lemon juice
2tbspmilk,(or buttermilk), plus more if needed
3cup(12 ounces) confectioners' sugar
For the cake: Adjust your oven rack to lower-middle position. Preheat the oven to 350F. Brush the pan with melted butter, making sure to get into any nooks and bends in the design. Dust the pan liberally with flour and then tap out the excess.
Combine the lemon zest and lemon juice in a small bowl; set aside to soften, 10 to 15 minutes.
In a large bowl, whisk together the flour, baking power, baking soda and salt. In a medium bowl, whisk the lemon juice mixture with the vanilla extract and yogurt. In a small bowl, whisk the eggs and yolk to combine.
Using a standing mixture fitted with the flat beater, cream the butter and sugar together on medium-high speed until light and fluffy, about 3 minutes. Scrape down the sides of the bowl with a rubber spatula. Add the eggs and mix together on medium speed until incorporated, about about 20 seconds, scraping down the bowl as needed.
Now it's time to mix in the flour and the yogurt. Turn the mixer on low; add 1/3 of the flour mixture and mix until just incorporated. Then add 1/2 of the yogurt mixture, again mixing until just incorporated. Continue adding in turns - 1/3 of the flour, the remain 1/2 of the yogurt, and the last 1/3 of the flour. When the last of the flour is almost mixed in, remove the bowl from the mixer and use your spatula to give the batter a few swift stirs to finish mixing. (If you don't have a standing mixer, you can use a hand mixer. Just increase the mixing time for the butter and sugar to 6-7 minutes.)
Dollop the batter into the prepared pan, adding spoonfuls evenly around the circle of the Bundt pan. Pour the blueberries over the top and push gently into the top of the batter. This will keep them all towards the bottom of the cake. If you prefer the blueberries be more evenly distributed, mix half the blueberries into the batter before putting it in the pan and add the other half to the top of the batter as above.
Bake until the cake is golden brown and a wooden skewer or toothpick inserted into center comes out with no crumbs attached, 55-65 minutes.
Put the bundt pan on a wire rack and let the cake cool in the pan for 30 minutes. Then gently loosen the cake from the edges of the bundt pan with a butter knife or spatula and invert cake directly onto the rack. If the cake doesn't want to get out of the pan, try loosening it again and tapping the pan. With a complicated Bundt design, this may take a few tries. Let the cake cool completely before glazing.
For the glaze: Whisk together the lemon juice, milk, and confectioners' sugar until smooth and very thick. The glaze should be just liquid enough to flow thickly off the whisk. If it doesn't flow, add more milk by the 1/2 tablespoon until it does. Spoon the glaze evenly over the top of the cooled cake until it looks like there is enough on it. Don't worry if it doesn't look smooth and pretty at first; the glaze will slowly work its way down the cake. Cut into slices and serve.
For best results let the eggs, milk, and yogurt come to room temperature before you make the batter. With cold ingredients the center takes a long time to cook through.To quickly warm the eggs put them in some warm water for a few minutes.DO NOT use more than 2 cups of blueberries.In place of the plain yogurt you can substitute 1/2 cup of Greek yogurt (whole milk, or low fat with no stabilizers) plus 1/4 cup milk, or 3/4 cup buttermilk.Cool room temperature for butter is 60F. The butter should be cool, but pliable, and not soft. To quickly bring butter to temperature, cut it into 1/4 inch pieces and let it sit at room temperature for about 10 minutes.