Heat the oven to 375°F. Lightly grease eight cups of a standard muffin tin.
Combine the rinsed quinoa and water in a saucepan. Bring to a boil, then cover and reduce the heat to low. Cook until the water is absorbed and the quinoa is tender, about 15 minutes. Remove it from the heat and keep it covered.
In a large bowl, combine the ground turkey, egg, rolled oats, onion, ¼ cup of the BBQ sauce, smoked paprika, garlic powder, salt, and black pepper. Mix gently until just combined.
Divide the turkey mixture among the eight prepared muffin cups. Bake until the muffins are cooked through, about 20 to 25 minutes. Brush the tops with the remaining ¼ cup BBQ sauce during the last 5 minutes of baking.
Stir the Greek yogurt and lemon juice together in a small bowl. Set it aside for serving.
Divide the cooked quinoa among four bowls. Add the cucumber, cherry tomatoes, and red bell pepper. Place two turkey meatloaf muffins in each bowl, then finish with the yogurt sauce and chopped parsley.