Heat olive oil in a sauté pan over medium high heat and cook carrots, onions, and garlic for 8 to 10 minutes or until softened.

In a food processor, combine carrot mixture with rice, bread crumbs, zucchini, mushrooms, egg, chili flakes, salt, coriander, and paprika. Pulse to chop and combine until a coarse mixture is formed.

Form 4 (1-cup) patties and place on a greased sheet pan. Cover with plastic wrap and refrigerate at least 1 hour, or overnight.

Preheat grill pan or sauté pan over medium high heat. Cook burgers for 6 to 8 minutes per side or until golden brown and heated through. Place each burger on a challah roll with 1 tablespoon each Herbed Honey Mustard and feta.