01 - Heat olive oil in a skillet over medium-low heat. Add sliced onions and salt. Cook, stirring occasionally, until deeply caramelized and golden brown, about 20 to 25 minutes. Remove from heat and set aside to cool completely.
02 - In a large bowl, whisk together sourdough starter, warm water, and honey until fully dissolved. Add bread flour, whole wheat flour, and salt. Stir until a rough, shaggy dough forms.
03 - Turn dough onto a lightly floured surface and knead for 8 to 10 minutes until smooth, elastic, and no longer sticky. Shape into a ball.
04 - Place dough in a lightly oiled bowl, cover with plastic wrap or a damp towel, and let rest at room temperature for 4 to 6 hours until doubled in size.
05 - Turn dough onto a floured surface and divide into 8 equal portions. Roll each piece into a tight ball. Poke your thumb through the center and gently stretch to form a ring with a 2-inch hole.
06 - Place shaped bagels on a parchment-lined baking sheet. Cover loosely and proof at room temperature for 1 hour, then refrigerate overnight for 8 to 12 hours.
07 - Preheat oven to 425°F. Bring 8 cups water and barley malt syrup (or honey) to a gentle boil in a large saucepan.
08 - Remove bagels from refrigerator. Working in batches, boil bagels for 45 seconds per side using a slotted spoon. Transfer back to the baking sheet.
09 - Press caramelized onions gently onto the tops of boiled bagels to adhere.
10 - Bake for 20 to 25 minutes until deeply golden brown, crispy on the outside, and cooked through. Rotate pan halfway through for even browning.
11 - Transfer bagels to a wire rack and let cool completely before slicing and serving.