In a large bowl whisk together flour, sugar, baking powder, baking soda, and 1 teaspoon salt. Make a well in the center of the bowl.
In a medium bowl whisk together eggs, buttermilk, 1 1/2 cups milk, butter, and 2 teaspoons vanilla.
Add all of the wet ingredients to the dry ingredients at once and stir until just combined. Cover and let rest 15 minutes.
Meanwhile, grease three 8- or 9-inch round cake pans. Line the bottoms with parchment paper. Grease and flour the pans. Transfer about 1-1/4 cups of batter into each pan. Sprinkle each with 1/2 cup blueberries. Repeat with remaining batter and blueberries.
Bake for 30 to 40 minutes or until a toothpick inserted near the center of the cake comes out clean. Let cool in pan on wire rack for 5 minutes. Remove cakes from pan and cool completely.
In the bowl of a stand mixer fitting with the paddle attachment, combine butter and half of the powdered sugar. Add 1/2 cup maple syrup, 1 tablespoon vanilla, and kosher salt. Gradually add remaining powdered sugar. Add milk, 1 teaspoon at a time, to reach desired consistency.
If desired, slice cake layers in half lengthwise. Stack cake layers on a serving platter or cake stand with frosting in between each layer. Spoon a large dollop of frosting on the top and sprinkle with additional blueberries. Drizzle with remaining maple syrup and top with white chocolate squares, if desired.