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 and browned, about 20 to 25 minutes. Remove from heat and set aside to cool completely.
02 - In a large mixing bowl, combine sourdough starter, warm water, and honey. Stir until honey dissolves completely. Add bread flour, whole wheat flour, and sea salt. Mix with a wooden spoon until a rough, shaggy dough forms.
03 - Turn dough onto a lightly floured surface. Knead firmly for 8 to 10 minutes, pushing forward with the heel of your hand and folding back, until dough is smooth, elastic, and springs back when poked. Place in a lightly oiled bowl, cover with plastic wrap, and let rise at room temperature for 4 to 6 hours until doubled in size.
04 - Punch down risen dough and transfer to a floured surface. Divide into 8 equal portions. Roll each piece into a tight ball between your palms. Poke your thumb through the center of each ball and gently stretch to form a ring with a 2-inch hole. Arrange on a parchment-lined baking sheet, cover loosely with a kitchen towel, and proof at room temperature for 1 hour, then refrigerate overnight for 8 to 12 hours.
05 - Preheat oven to 425°F. Arrange oven rack in the center position.
06 - Bring 8 1/2 cups water and 1 tablespoon barley malt syrup (or honey) to a gentle boil in a large saucepan or Dutch oven. Reduce heat to maintain a steady simmer.
07 - Remove bagels from the refrigerator. Working in batches, carefully lower bagels into the simmering water using a slotted spoon. Boil for 45 seconds per side, flipping once. Transfer boiled bagels back to the parchment-lined baking sheet.
08 - Press caramelized onions gently onto the tops of boiled bagels to adhere. Bake for 20 to 25 minutes until deeply golden brown, glossy, and crisp, rotating the baking sheet halfway through for even browning.
09 - Transfer baked bagels to a wire cooling rack. Let cool for at least 30 minutes before slicing to prevent the interior from becoming gummy. Slice horizontally and serve toasted with cream cheese or your desired spreads.