Preheat the oven to 400 degrees F (200 degrees C). Line a large rimmed baking sheet with aluminum foil.

Combine broccoli, cauliflower, and cabbage in a large bowl. Whisk olive oil, salt, and paprika together in a measuring cup and pour over vegetables. Gently stir until all of the vegetables are coated. Set aside.

Combine chili powder, cumin, and garlic powder on a flat plate. Roll each chicken thigh in the spice mixture so that both sides are coated. Wrap 2 pieces of bacon around each thigh and place chicken in the center of the baking sheet.

Stir vegetables one last time and scatter them around the chicken in an even layer.

Bake in the preheated oven until bacon is crispy and chicken is no longer pink in the center and the juices run clear, 35 to 40 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).