Preheat your oven to 400°F.
Place the chicken in a pot of water and bring to a boil. Cook until the chicken is fully cooked through. Remove from the water, allow it to cool slightly, and shred.
While the chicken cooks, prepare everything else. Cut the kielbasa lengthwise in half, then slice into bite-sized pieces. Wash and chop the red potatoes, yellow zucchini, and bell peppers into bite-sized pieces. Peel and dice the red onion.
Combine everything all into 1 bowl - even the shredded chicken. Add in the brown sugar and spices, toss until everything is coated.
Spread the mixture onto a foil-lined sheet pan, arranging everything in an even layer.
Bake at 400°F for approximately 25 minutes, or until the vegetables and potatoes are tender and everything is heated through.
Serve warm with a sprinkle of Parmesan cheese, if desired. I recommend it!