Pound the chicken even: Place the chicken breasts between two sheets of plastic wrap and pound the thicker end to an even half-inch thickness. This helps the whole piece cook at the same rate.
Season the chicken: Pat the chicken dry with paper towels, then rub with 1 tablespoon olive oil, paprika, 1/2 teaspoon salt and 1/4 teaspoon pepper on both sides.
Sear until golden: Heat a skillet over medium-high heat and cook the chicken for about 5 minutes per side, until deep golden brown and no longer pink in the center.
Rest and slice: Transfer the chicken to a cutting board and let it rest for 5 minutes before slicing against the grain into strips.
Start the rice: Combine the brown rice and water in a saucepan, bring to a boil, then cover and simmer on low for 35 to 40 minutes until tender and the water is absorbed.
Roast the vegetables: Toss the broccoli and bell pepper with the remaining tablespoon of olive oil, 1/2 teaspoon salt and 1/4 teaspoon pepper. Spread on a sheet pan and roast at 425°F for 15 to 18 minutes until the edges turn brown and slightly crisp.
Make the sauce: Stir together the Greek yogurt, minced garlic and lemon juice in a small bowl until smooth and creamy.
Assemble the bowls: Divide the cooked rice, roasted vegetables and sliced chicken evenly among four containers.
Add sauce and finish: Spoon the lemon garlic yogurt sauce over each bowl and sprinkle with chopped parsley if using before sealing the containers.