Butter an 8-inch square baking dish; set aside. Microwave 3 tablespoons of the butter in a small microwave-safe bowl or liquid measure to melt, 30 seconds to 1 minute.
Whisk together the flour, 3 tablespoons of the granulated sugar, baking powder, baking soda and 1/2 teaspoon salt in a large bowl. Whisk together the buttermilk, 2 of the eggs and the melted butter in a small bowl. Add the wet ingredients to the dry ingredients, and stir until just combined.
Heat a large nonstick skillet or griddle over medium heat; melt a little of the remaining tablespoon butter in the skillet. Working in batches, spoon 1/4 cup of batter per pancake into the skillet, and cook until the bottom is golden brown and small bubbles appear on the top, 2 to 3 minutes; flip and cook until golden brown on the other side, about 2 minutes. If the pancakes brown too quickly, reduce the heat to medium-low. Transfer the cooked pancakes to a plate. Repeat until all the batter is used, adding more butter to the pan as necessary. (You should have at least 12 pancakes.)
Whisk together the half-and-half, vanilla, the remaining 5 eggs and 3 tablespoons granulated sugar and 1/4 teaspoon salt in a large bowl.
Shingle half the pancakes in the prepared baking dish. Scatter half the sliced bananas and chocolate chips over the pancakes. Pour half the egg mixture evenly over the pancakes. Repeat with the remaining pancakes, bananas, chocolate chips and egg mixture. Cover the dish with plastic wrap, and refrigerate for at least 8 hours and up to overnight to allow the pancakes to soak in the custard.
Preheat the oven to 350 degrees F. Remove the plastic wrap, cover the dish loosely with foil and bake for 30 minutes. Uncover and continue to bake until golden brown, the custard is set and the center feels firm but springy, about 30 minutes more. Let cool 15 minutes. Dust with confectioners' sugar.