In a large bowl, toss butter, Parmesan, cheddar, flour, paprika and 1/2 teaspoon black pepper with fingers until combined.
Using hands, press mix into a dough. Roll dough into a log 2 1/4 inches in diameter. Tightly wrap in parchment paper. Twist ends of parchment to keep log tight. Chill 45 minutes or until just firm.
Adjust oven racks to lower and upper middle positions and preheat to 350°F Line 2 baking sheets with parchment paper.
Remove paper from log and slice into 1/8-inch-thick slices. Space evenly on pans. Sprinkle with smoked salt and bake until a deep golden brown, about 15 minutes; about halfway through, rotate pans from top to bottom and front to back.