In a large mixing bowl, combine the all-purpose flour, bread flour, sugar, and salt. Mix well.

Add the active sourdough starter and warm water to the dry ingredients. Stir until a shaggy dough forms.

Knead the dough on a floured surface for about 8-10 minutes until smooth and elastic.

Gently fold in the mashed raspberries and chopped pistachios until evenly distributed.

Place the dough in a lightly greased bowl, cover with a damp cloth, and let it rise at room temperature for 4-6 hours, or until doubled in size.

Once risen, punch down the dough and divide it into 8 equal pieces. Shape each piece into a ball and then poke a hole in the center to form a bagel shape.

Place the shaped bagels on a parchment-lined baking sheet and let them rest for 30 minutes.

Preheat your oven to 425°F. In a large pot, bring water to a boil and add the baking soda.

Boil each bagel for about 1 minute on each side, then return them to the baking sheet.

Beat the egg and brush it over the top of each bagel for a shiny finish.

Bake in the preheated oven for 20-25 minutes or until golden brown.

Allow to cool on a wire rack before serving.