Combine first 4 ingredients in a large bowl. Stir in 1 tablespoon mint, 1 tablespoon thyme, 1/4 teaspoon salt, allspice, and next 3 ingredients (through egg). Press meat mixture into 8 muffin cups coated with cooking spray. Bake at 450° for 7 minutes. Turn broiler to high; broil 3 minutes.
Combine yogurt, feta, 1 tablespoon juice, 1 teaspoon mint, and 1 teaspoon thyme in a mini food processor; pulse 10 times to combine.
Combine 1 tablespoon juice, oil, 1/8 teaspoon salt, and pepper in a bowl; stir. Add arugula and cucumber; toss.
MyRecipes is working with Let's Move!, the Partnership for a Healthier America, and USDA's MyPlate to give anyone looking for healthier options access to a trove of recipes that will help them create healthy, tasty plates. For more information about creating a healthy plate, visit www.choosemyplate.gov.