To spatchcock the turkey, place it breast-side down on a cutting board. Using sturdy poultry shears, cut along both sides of the backbone to remove it. Flip the turkey over and press firmly on the breastbone with the heel of your hand until you hear a crack and the bird lies flat.
In a large pot or brining bag, combine the cold water, kosher salt, and brown sugar. Stir until the salt and sugar are fully dissolved. Submerge the spatchcocked turkey in the brine, ensuring it is fully covered. Refrigerate for 8 to 12 hours.
Remove the turkey from the brine and discard the brine. Rinse the turkey thoroughly inside and out with cold water. Pat the turkey completely dry with paper towels. For the crispiest skin, place the turkey on a wire rack set over a baking sheet and refrigerate, uncovered, for at least 2 hours or up to overnight to air-dry the skin.
Preheat your oven to 425°F (220°C). Place an oven rack in the lower-middle position. In a small bowl, combine the softened butter, parsley, thyme, chives, and minced garlic. In a separate small bowl, mix together the smoked paprika, black pepper, onion powder, and garlic powder to create the rub.
Gently slide your fingers between the skin and the meat of the breasts and thighs to create pockets. Spread about half of the herb butter mixture directly onto the meat under the skin. Rub the remaining herb butter all over the outside of the skin. Sprinkle the spice rub evenly over the entire turkey.
Place the turkey on a wire rack set inside a large, rimmed baking sheet. Transfer to the preheated oven.
Roast for 70 to 90 minutes. The turkey is ready when an instant-read thermometer inserted into the thickest part of the breast registers 160°F (71°C) and the thickest part of the thigh registers at least 170°F (77°C).
Carefully transfer the turkey to a large cutting board. Let it rest for 15 to 20 minutes before carving. The internal temperature of the breast will continue to rise to a safe 165°F (74°C) during this time. Carve and serve.