01 - Heat olive oil in a skillet over medium-low heat. Add sliced onions and 1/2 teaspoon salt. Cook, stirring occasionally, until deeply caramelized for about 20-25 minutes. Set aside to cool completely.
02 - In a large bowl, combine the sourdough starter, warm water, and honey. Stir until dissolved. Add bread flour, whole wheat flour, and salt. Mix to form a rough dough.
03 - Turn dough onto a lightly floured surface and knead for 8-10 minutes until smooth and elastic. Place in a lightly oiled bowl, cover, and let rest at room temperature for 4-6 hours until doubled in size.
04 - Divide dough into 8 equal pieces. Shape each piece into a tight ball. Poke a hole through the center with your finger and gently stretch to form a bagel shape with a 2-inch hole. Place on a parchment-lined baking sheet.
05 - Cover shaped bagels loosely and let proof at room temperature for 1 hour, then refrigerate overnight for 8-12 hours to develop flavor.
06 - Preheat oven to 425°F.
07 - Bring 8 1/2 cups water and 1 tablespoon barley malt syrup (or honey) to a gentle boil in a large saucepan.
08 - Remove bagels from the refrigerator. Boil each bagel for 45 seconds per side, then transfer back to the baking sheet with a slotted spoon.
09 - Immediately top boiled bagels with caramelized onions, pressing gently to adhere.
10 - Bake for 20-25 minutes until golden brown and crisp.
11 - Transfer bagels to a wire rack and let cool completely before slicing and serving.