Place the bulgur and 1/2 teaspoon salt in a medium bowl and add the boiling water. Soak until tender but slightly chewy, 20 minutes. Strain to remove any excess moisture.
Heat a large nonstick skillet with 2 tablespoons of the olive oil over medium heat. Add the onions, 1/4 teaspoon salt and a pinch of black pepper. Cook, stirring, until soft and starting to brown, about 4 minutes. Add the cumin and allspice, and stir until very fragrant and the onions are evenly coated in the spices, about 1 minute. Transfer the onions to a large bowl to cool. Carefully wipe out the skillet to use again later.
Mix together the hummus, yogurt, 1 teaspoon of the lemon juice and 1/2 teaspoon salt.
Add the bulgur, ground beef, 1 1/4 teaspoons salt and 1/4 teaspoon pepper to the onions. Gently mix together and form 4 patties, each just under 1/2-inch thick.
Heat the reserved skillet with 1 tablespoon of the olive oil over medium heat. When the oil starts to shimmer, add the patties, making sure to leave some space between them. Cook until the patties are cooked through, 5 to 6 minutes per side.
Toss together the greens, pomegranate seeds, cucumber, the remaining 1 tablespoon lemon juice, the remaining 1 tablespoon olive oil and salt and pepper to taste in a large bowl. Divide the patties and salad among four plates. Serve each with pita and a dollop of the yogurt sauce.
Copyright 2015 Television Food Network, G.P. All rights reserved.