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Arrange a rack in the middle of the oven and heat to 425°F. Place a rimmed baking sheet in the oven while it is heating.
Whisk the honey, Dijon, whole-grain mustard, vinegar, pepper, and 1/2 teaspoon of the salt in a small bowl; set aside.
Place the potatoes, 1 tablespoon of the oil, and 1/4 teaspoon of the salt in a large bowl and toss to combine. Remove the baking sheet from the oven and arrange the potatoes in a single layer, cut-side down. Return to the oven and roast for 15 minutes. Meanwhile, place the chicken, broccoli, red onion, remaining 1 tablespoon oil and remaining 1/4 teaspoon salt in the same bowl and toss to combine.
Add the chicken, broccoli, and red onion to the baking sheet. Pour half the honey-Dijon mixture over the chicken and vegetables and toss to evenly coat them in the sauce. Spread the chicken and veggies into a single layer.
Roast for 10 minutes. Remove from the oven, toss with the remaining honey-Dijon mixture, and spread back into an even layer. Roast until the chicken is cooked through and the vegetables are tender, about 5 minutes more.