Heat 1 T. of olive oil in a large skillet over medium heat. Add turkey and brown until no longer pink.
Add brown sugar, soy sauce, ginger, garlic, sesame oil, and red pepper flakes. Stir to combine, reduce heat and simmer until turkey is cooked through.
Add shredded carrot and cook for a few more minutes until carrots are softened.
Meanwhile, mix spicy yogurt ingredients together in a small bowl and set aside in the refrigerator until ready to use.
Serve turkey and carrot mixture over brown rice, topped with spicy yogurt, sliced cucumber and scallions.