In a large mixing bowl, combine the all-purpose flour, bread flour, salt, and sugar. 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 lightly floured surface for about 8-10 minutes until smooth and elastic.

Gently fold in the raspberries and chopped pistachios, being careful not to crush the raspberries too much.

Place the dough in a lightly greased bowl, cover it with a damp cloth, and let it rise at room temperature for about 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. Cover and let them rest for 30 minutes.

Preheat the oven to 425°F. Bring a large pot of 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 bagels for a shiny finish.

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

Allow to cool on a wire rack before serving.