Lamb Burgers with Feta Spread

2 1/4 pounds ground lamb (10 percent fat)
1/2 cup minced shallots
3 tablespoons minced fresh mint leaves
1 tablespoon minced garlic
1 1/2 teaspoons salt
1/2 teaspoon ground cumin
1/4 teaspoon ground allspice
1/4 teaspoon cayenne pepper, plus 1/8 teaspoon
1/4 teaspoon ground cinnamon
4 ounces feta cheese, crumbled
4 ounces cream cheese, softened
1/4 cup mayonnaise
2 tablespoons minced green onion tops
1 tablespoon plus 1 teaspoon olive oil
1/4 teaspoon finely grated lemon zest
6 hamburger buns
Lettuce leaves, for garnish, optional
Thinly sliced tomatoes, for garnish, optional
Sliced roasted red peppers, for garnish, optional

In a mixing bowl, combine the lamb, shallots, mint, garlic, salt, cumin, allspice, 1/4 teaspoon of the cayenne, and the cinnamon and mix gently but thoroughly to combine. Using your hands, shape the mixture into 6 wide patties about 1/2-inch thick and transfer to a large plate or a platter. Cover with plastic wrap and refrigerate for at least 2 hours and up to overnight.

Make the feta dip: Combine the remaining 1/8 teaspoon cayenne pepper, feta cheese, cream cheese, mayonnaise, green onions, 1 teaspoon of the olive oil, and lemon zest in a mixing bowl and stir to blend well. Cover with plastic wrap and refrigerate for at least 1 hour and up to overnight to allow flavors to blend.

When ready to cook the burgers, preheat a grill to medium-high. Brush the burgers on both sides with the remaining tablespoon of olive oil. When the grill is hot, add the burgers and cook for about 4 minutes on each side for medium. Transfer the burgers to a platter and cover loosely with foil. Place the buns, cut sides down, and in batches if necessary, in the hot skillets and cook until warmed through and slightly toasted, about 2 minutes. Serve the buns with the cooked burgers and spoon some of the feta spread over each burger. Garnish with lettuce, tomatoes, and sliced roasted peppers if desired, and serve immediately.