Lemon Blueberry Cake

Name: Lemon Blueberry Cake
Ingredients: 2 sticks (8 ounces) unsalted butter; 4 large eggs; 1 1/2 cups whole milk; Cooking spray; 3 cups all-purpose flour; 2 teaspoons baking powder; 2 teaspoons vanilla extract; 2 cups granulated sugar; 2 medium lemons; 1 1/2 teaspoons kosher salt; 2 cups fresh or frozen blueberries (do not thaw, about 10 ounces), divided; 1 pound powdered sugar (about 4 cups); 1/4 cup lemon juice (from the lemons in the cake); 1/4 teaspoon kosher salt; 1 teaspoon vanilla extract