1. Preheat the oven to 400 degrees F. Using a fork, mash together the butter, Monterrey Jack, herbs, Parmesan, smoked paprika, 1 teaspoon salt and 1/4 teaspoon pepper in a medium bowl until combined. Spoon onto a piece of nonstick aluminum foil and, using one side to press, form into a 6-inch log. Wrap the foil around the log, twist the ends closed and place in the freezer until firm, about 20 minutes.
2. Using a sharp knife, cut a series of slits into each potato, with about 1/8-inch between slits and cutting about three-quarters of the way through. Unwrap the butter log and thinly slice two-thirds of it into about 24 rounds. Slip the butter slices into every 3 to 4 slits of each potato, using about 6 slices per potato. Wrap each potato tightly in nonstick aluminum foil, sealing the foil on the top side of the potato.
3. Place directly on the oven rack and bake until very tender, about 1 hour. Carefully open the top of each potato package to let out the steam and expose the tops. Bake until browned and crisped, about 10 minutes more. Unwrap each potato and drizzle with any accumulated flavored butter from the foil.