Pulse onions in 3 batches in a food processor until very coarsely chopped (there may be a few large pieces remaining), transferring to a bowl. Repeat with shallots, then garlic.
Heat oil in a deep 12-inch heavy nonstick skillet over high heat until it shimmers, then sauté onions, shallots, and garlic (stir often) until golden and browned in spots, 25 to 30 minutes
Grind fenugreek seeds in grinder or with mortar and pestle. Add to onion mixture along with remaining ingredients, and stir until combined.
Transfer to a parchment-paper-lined large 4-sided sheet pan and spread as thinly and evenly as possible. Bake, stirring occasionally with a skewer to separate onions, until well browned and barely moist, 1 to 1 1/4 hours.