Pat the ribeye steaks dry with paper towels and season both sides with kosher salt, cracked pepper, garlic powder, and paprika, pressing the seasoning into the meat.
If time allows, refrigerate the seasoned steaks uncovered for 4 to 48 hours to dry-brine. If not, let them rest at room temperature for 1 hour before cooking.
Remove the steaks from the refrigerator 60 minutes before cooking to come to room temperature if you dry-brined them.
Heat a cast iron skillet over high heat until smoking, then add 1 tablespoon oil and swirl to coat; reduce heat to medium-high and add the steaks.
Sear the steaks without moving for 3 minutes, then check for a deep golden crust; flip and sear the other side for 1 minute.
Flip again, add the halved garlic cut-side down, the rosemary and thyme, and the remaining 1 tablespoon oil; sear for 3 more minutes, then sear the edges about 30 seconds each.
Reduce heat to medium-low, add the butter, and baste the steaks with the melted butter for about 1 minute by tilting the pan and spooning the butter over the meat.
Continue cooking and basting until the steaks reach a temperature about 5°F below your desired final doneness (use a meat thermometer). Refer to the guide: medium-rare 130°–140°F, medium 140°–145°F, medium-well 150°–160°F.
Transfer the steaks to a plate or cutting board, baste once more with the pan butter, loosely tent with foil, and rest for 10 minutes before slicing against the grain.
While the steaks rest, reserve 1 tablespoon of the cherry juice in a small bowl and whisk in the chicken broth and cornstarch to form a slurry.
Drain all but about 2 tablespoons of pan butter/drippings from the skillet, leaving the garlic and herbs in the pan. Add the minced shallot and sauté until softened, about 3–5 minutes.
Stir in the cherry–broth slurry and simmer 2–3 minutes until thickened, scraping up browned bits from the pan.
Add the canned tart cherries (with reserved juices set aside), honey, Dijon mustard, brown sugar, and balsamic vinegar; gently simmer until warmed and sauce is combined, then season with salt and pepper to taste.
Spoon the tart cherry sauce over the sliced ribeye and serve.