Stir the cumin, coriander, salt, pepper, allspice and nutmeg together in a small bowl to blend.
Make the yogurt sauce
Stir the feta and yogurt together in a bowl.
Mix the slaw
Toss the fennel in a bowl with the lemon juice, olive oil and ½ teaspoon salt.
Lamb burgers
Preheat a grill to medium-high for direct grilling.
Put the lamb in a large bowl. Grate the onion on a box grater and add to the lamb. Add the spice mix. Blend well with your hands or a large fork and form into 4 patties.
Grill or broil the burgers until cooked to your liking, about 3 minutes per side for medium-rare.
Serve the burgers on buns or pita, topped with some of the feta-yogurt sauce, fennel slaw, green sauce, lettuce, cucumber and sprouts.
Notes
The yogurt sauce and slaw can be prepped and refrigerated up to 6 hours ahead.
Season the lamb and shape the burgers up to 6 hours ahead. Put them on a lightly oiled plate or baking sheet, cover and keep refrigerated. Bring them to room temperature for about 15 minutes before cooking.