Preheat oven to 400°F (205°C). In a small bowl, thoroughly mash together softened butter, minced garlic, chopped rosemary, thyme, sage, Dijon mustard, smoked paprika, 1/2 teaspoon kosher salt, and black pepper until completely blended into a fragrant compound butter.

Pat turkey tenderloins thoroughly dry with paper towels; season both sides with remaining salt and pepper. Heat 1 tablespoon olive oil in a heavy 12-inch oven-safe cast iron skillet over medium-high heat. Sear tenderloins undisturbed for 2 to 3 minutes per side until a deep golden-brown crust develops.

Remove skillet from heat. Generously slather the garlic herb compound butter all over the tops of both seared tenderloins. Transfer the skillet directly into the preheated oven. Roast for 18 to 22 minutes, until an instant-read thermometer inserted into the thickest center registers 165°F (74°C).

Carefully transfer the roasted tenderloins to a cutting board, tent loosely with aluminum foil, and let rest for 8 minutes so juices redistribute. Place the skillet back on the stovetop over medium heat. Pour in chicken bone broth, scraping up all the golden caramelized herb drippings from the pan bottom. Simmer for 2 to 3 minutes until reduced by half. Remove from heat and vigorously whisk in 1 tablespoon cold butter until glossy and velvety.

Carve the tenderloins against the grain into thick, succulent medallions. Fan medallions on warm serving plates, spoon the rich pan herb butter gravy over top, and garnish with fresh rosemary and thyme sprigs. Serve immediately with creamy mashed potatoes and cranberry sauce.