Place the blueberries in a small saucepan over low heat. Warm them for 2-3 minutes until they start to burst and become juicy. Remove from heat and let cool.

In a large bowl, combine 1 1/4 cups warm water, 2 1/4 teaspoons active dry yeast, and 2 tablespoons granulated sugar. Stir and let sit for 5 minutes until the mixture is frothy.

Add 5 cups of bread flour, 1 1/2 teaspoons of salt, and 1/2 teaspoon of vanilla extract to the yeast mixture. Stir until a thick, slightly sticky dough forms. If needed, add a tablespoon of water at a time to bring the dough together.

Turn the dough onto a lightly floured surface and knead for about 7-10 minutes until the dough is smooth and elastic. Gently fold in the blueberries during this process.

Form the dough into a ball and place it in a lightly oiled bowl. Cover with a damp towel and let it rise in a warm spot for about 1 hour until doubled in size.

Punch down the dough and divide it into 8 equal pieces. Roll each piece into a ball. Using your thumb, poke a hole in the center of each ball and gently stretch the hole to form a bagel shape. Let the shaped dough rest for 15 minutes.

Preheat the oven to 425°F. Line one or two baking sheets with parchment paper and place the boiled bagels on them. Brush the bagels with egg white. Bake for 15-25 minutes, rotating the pan halfway through, until they are a nice golden brown.

Remove the bagels from the oven and let them cool on a wire rack for about 30 minutes before serving.