In a medium bowl, whisk together ½ cup honey, ¼ cup yellow mustard, and ¼ cup Dijon mustard until smooth. Taste and adjust the balance by adding a little more honey or mustard if desired; set the sauce aside.
Pat about 1.25 pounds boneless skinless chicken breasts (or tenders) dry. Season both sides with ½ teaspoon salt and ½ teaspoon pepper.
Heat a large skillet over medium-high heat. Add 2 tablespoons olive oil and heat until the oil shimmers.
Add the chicken to the skillet in a single layer. Cook undisturbed about 3 to 5 minutes on the first side, then flip and cook about 3 to 5 minutes on the second side, until the chicken is mostly cooked through (about 90% cooked). Actual time will vary with thickness.
Evenly drizzle the reserved honey-mustard sauce over the chicken. Flip each piece a few times so both sides are coated with the sauce.
Add 2 to 3 cups broccoli florets to the skillet and stir to combine, making sure the broccoli is coated with the sauce.
Cover the skillet, reduce heat to medium-low, and steam for about 3 to 5 minutes, or until the broccoli is crisp-tender and the chicken is cooked through (internal temperature 165°F / 74°C or no visible pink in the center).
Remove from heat and serve immediately.