Pre-heat a large 12" nonstick skillet over medium-high heat. Season the chicken with salt and pepper. Add the olive oil to the pan and sauté the chicken pieces until well browned on all sides, about 8 minutes per side.
Combine the honey, brown sugar, soy sauce, and Dijon mustard in a small bowl and whisk until the brown sugar has started to dissolve and the glaze is smooth.
Remove the chicken temporarily from the skillet, drain and discard any excess grease, then return the chicken to pan. Pour the glaze over the chicken. Lower the heat and simmer the chicken and sauce together until the sauce thickens and the chicken has cooked through, about 15 minutes. During the cooking process, turn the chicken over a few times to coat the chicken with the glaze. (Alternately, transfer the pan to a pre-heated 400°F oven for 10 to 15 minutes, watching to make sure the glaze doesn't burn.)
Let the chicken rest for a few minutes before transferring to a serving dish. Pour the glaze over chicken and serve with scallions on top.
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