Preheat oven to 350F (176C) with rack in middle position.

Pulse onions in a food processor in 3 batches until very coarsely chopped.

Transfer chopped onions to a bowl.

Repeat the pulsing process with shallots, then garlic.

In a deep 12-inch heavy nonstick skillet over high heat, heat vegetable oil until it shimmers.

Sauté onions, shallots and garlic (stir often) until golden and browned in spots, about 25-30 minutes.

In an electric coffee/spice grinder, or with mortar and pestle, grind fenugreek seeds.

Add ground fenugreek to onion mixture and add remaining ingredients. 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.

Store in a tightly sealed container in the refrigerator for up to 1 month or in the freezer for up to 6 months.