Preheat your oven to 350 degrees F. Grease a 9x5 loaf pan. See notes if you have a dark pan.
In a medium bowl, peel and mash the bananas.
Brown the butter: In a small pan, heat the butter on medium and melt it, letting it continue to cook just until it turns the color of caramel. (It should take about 4 minutes, but keep a close eye on it so it doesn't burn.) Immediately stir the brown butter into the mashed bananas. (Don't let the brown butter sit in the pan, or it'll burn.)
Stir the egg and liqueur into the banana mixture, making sure the egg is blended. Then, stir in the brown sugar.
In a small mixing bowl, use a spoon to mix the flour, cinnamon, baking soda and salt. Add these dry ingredients to the banana mixture and stir to combine. Stir in the white chocolate chips.
Transfer the batter to your loaf pan and tap the pan on the counter to remove any air bubbles. Bake at 350 degrees F for 55-60 minutes, covering loosely with foil after 45 minutes to prevent over-browning. The bread is done when a cake tester or toothpick inserted in the middle comes out clean, with just a few crumbs.
Let the banana bread cool in the pan on a wire rack for 15 minutes. Transfer it to a serving plate by first placing a dish over the bread and inverting it onto the dish. Then, place your serving plate over the upside down bread and invert again.
Store, covered with foil, at room temperature for 4-5 days, if it lasts that long. (Or, you could cool the bread completely, wrap it in foil and freeze it in a freezer bag. For best taste, use it within three months, but it won't ever spoil.)
If using a dark loaf pan, the bread will brown more quickly. Check on it after 45 minutes of baking and test to see if it's done by inserting a toothpick or cake tester. If it comes out clean, with just a few crumbs, it's done.Substitutions:
White whole wheat flour works well here in place of all-purpose flour.
If you don't have hazelnut liqueur such as Frangelico, try using bourbon or amaretto. If you need to skip the alcohol, try using 1 ½ teaspoons of almond extract instead.
I've only tested this recipe with white chocolate chips, but you could try milk chocolate or semi-sweet chocolate chips as a substitute. You're going to want some sweetness here. Keep in mind, you may lose some of the marshmallow taste the white chocolate brings in combination with the other ingredients.