Remove the prime rib from the refrigerator and let it come to room temperature, about 1 hour before cooking. Preheat the oven to 450°F (232°C).

In a small bowl, mix together the smoked paprika, crushed toasted coriander seeds, kosher salt, black pepper, minced garlic, chopped rosemary, and chopped thyme. Rub the olive oil all over the prime rib, then generously apply the spice mixture, ensuring it covers all sides of the roast.

Place the seasoned prime rib on a roasting rack in a roasting pan. Roast in the preheated oven for 20 minutes, then reduce the temperature to 325°F (163°C) and continue to cook for about 1.5 to 2 hours, or until a meat thermometer inserted into the thickest part reads 130°F (54°C) for medium-rare. Once done, remove the roast from the oven and let it rest for at least 20-30 minutes before slicing.

In a medium skillet over medium heat, melt the softened butter. Add the sliced shallots and cook, stirring frequently, until they are golden brown and caramelized, about 10-15 minutes. Stir in the chopped sage and balsamic vinegar, and season with salt and pepper to taste. Remove from heat and let cool.

Slice the rested prime rib and serve topped with the browned shallot confit butter.