Preheat the oven to 450 degrees.

Combine the flour, salt, and pepper in a shallow bowl. Remove the tenders on the underside of the chicken breasts and save for another use. Heat the canola oil and 4 tablespoons of the butter together in a large cast-iron skillet over medium heat until the butter has melted and begins to sizzle. Dredge the chicken in the flour mixture and shake off any excess. Place the chicken, skin side down, in the skillet and cook over medium heat without moving for 12 minutes. With the chicken still skin side down, place the skillet in the oven and roast for 10 minutes. Return the skillet to the stovetop over medium heat. Turn the chicken skin side up, add the remaining 5 tablespoons of butter, and continue cooking for 3 to 5 minutes, until the butter is a nutty brown color and the chicken breasts are just cooked through. Off the heat, sprinkle on the parsley.

In a large saucepan, bring 2 quarts of water to a boil. Add salt and the orzo. Return the water to a boil and simmer uncovered for 9 to 11 minutes, until the orzo is al dente. Drain.

Transfer the orzo to a bowl and stir in the lemon zest, lemon juice, olive oil, dill, salt, and pepper. Fold in the feta and serve hot.

Divide the Lemon Orzo with Feta among four dinner plates. Transfer the chicken to a cutting board and slice each breast crosswise in thick slices. Arrange one breast on each plate with the orzo. Spoon a few tablespoons of the brown butter over each chicken breast, squeeze on some lemon, and sprinkle with salt. Serve hot with a fresh wedge of lemon on each plate.