Combine 1 cup of warm water with 2 teaspoons of active dry yeast and 1 tablespoon of brown sugar in a measuring cup. Stir gently and let it sit for about 10 minutes until bubbles form.

Mash enough overripe bananas to yield 1 ½ cups of banana puree, mixing in the remaining 2 tablespoons of brown sugar until combined.

In a large bowl, whisk together 4 cups of all-purpose flour, 1 cup of chopped walnuts, and 1 teaspoon of salt. Create a well in the center, pour in the yeast mixture and banana mash, then stir until a shaggy dough forms.

Knead the dough on a floured surface for about 5 to 10 minutes until smooth and elastic.

Place the kneaded dough in a greased bowl, cover, and let it rise in a warm place for approximately 1 hour until doubled in size.

Punch down the dough, divide into 8 portions, shape into balls, and poke a hole in the center of each to form bagels. Allow to rise for an additional 10 minutes.

Bring 6 cups of water to a boil, add 2 tablespoons of brown sugar, and boil each bagel for 1 minute on both sides. Remove and place on a parchment-lined baking sheet.

Preheat oven to 350°F (175°C). Brush boiled bagels with egg wash if using, sprinkle with pearl sugar, and bake for 35 to 45 minutes until golden brown.