Preheat the oven or grill for cooking on indirect heat at 425 degrees F. Line a baking sheet with nonstick aluminum foil.
Combine the baby carrots, honey, olive oil, Italian seasoning, Brussels sprouts, potatoes, lemon zest, salt, pepper and juice of 1/2 lemon in a large bowl. Toss to coat and distribute evenly around the edges of the lined baking sheet.
Place the hens in the middle of the baking sheet. Brush each hen with olive oil all over, then sprinkle with salt, pepper and Hungarian paprika to taste. Stuff each hen with the rosemary and thyme.
Place the baking sheet on the center rack of the oven or above the indirect heat of the grill. Roast until the hens reach an internal temperature of 155 degrees F and the veggies are caramelized, 30 to 40 minutes. Remove from the grill or oven and allow the hens to rest until they reach an internal temperature of 165 degrees F, about 5 minutes. Spritz with juice from the remaining lemon half before serving.