Prep the chicken. Remove any giblets or neck pieces from the cavity of your chicken, then pat it dry all over with paper towels. Set the chicken on a rimmed baking sheet lined with parchment paper.
Make the spice rub. In a small bowl, mix together the kosher salt, pepper, paprika, thyme, and sage. Season the chicken liberally all over, inside and out, with the seasoning mixture. Transfer the chicken on the baking sheet to the fridge uncovered for 8-24 hours.
Preheat your dutch oven. Preheat an oven to 375 F. Place a large dutch oven with the lid in the oven to preheat for 30 minutes.
Stuff the chicken. Remove the chicken from the fridge. Stuff the cavity with the lemon halves, garlic head, and rosemary sprigs. Truss the legs and tuck the wings behind the body.
Prep the veggies. In a mixing bowl, toss the onions, carrots, and potatoes with half of the melted butter. Season liberally with salt and pepper. Carefully remove the dutch oven from the oven and remove the lid. Spread the veggies into the bottom of the dutch oven and place the chicken on top. Brush the top of the chicken all over with the rest of the melted butter.
Roast the chicken. Cover the dutch oven and return to the oven for 35 minutes. Uncover, increase the temperature to 425 F, and cook for another 30-40 minutes, or until the chicken registers 165 F on an instant read thermometer. Let the chicken rest for 15 minutes before slicing and serving with the veggies.