Preheat the oven to 400°F (200°C). Line two rimmed baking sheets with parchment paper.
Place the chopped sweet potatoes on one baking sheet.
Pat the chicken thighs dry with paper towels and arrange them flat on the second baking sheet.
Scatter the chopped turkey ham around the chicken.
Place the chopped broccoli in a large bowl and set aside.
Drizzle olive oil over the sweet potatoes, chicken, and turkey ham.
In a small bowl, combine salt, black pepper, smoked paprika, garlic powder, onion powder, and brown sugar.
Sprinkle the seasoning mixture evenly over the chicken and sweet potatoes. Toss gently to coat.
Roast the sweet potatoes and chicken in the oven for 20 minutes.
Remove the pans from the oven. Toss the sweet potatoes and add the broccoli to the vegetable pan. Drizzle the broccoli with a little olive oil and season lightly.
Return everything to the oven and continue cooking for about 5–10 minutes, or until the chicken reaches an internal temperature of 165°F (74°C).
Remove from the oven and allow the chicken to rest for a few minutes.
Assemble the Hot Honey Chicken Bowls by dividing the sweet potatoes, broccoli, chicken, and turkey ham among serving bowls.
Drizzle generously with hot honey and sprinkle with red pepper flakes if desired.