Line 2 baking sheets with parchment paper. Mix Parmesan with choice of with cheese seasoning in a small bowl and set aside. Roll out one thawed but cold puff pastry sheet to roughly a 12 x 9 inch rectangle. Use a little flour on the work surface if dough sticks.
Melt 2 Tbsp. of the butter. Brush sheet lightly with some of the melted butter, sprinkle generously with cheese mixture, then roll lightly to press cheese into dough. Fold dough in half so short ends come together. Roll again into roughly a 12 x 9 inch rectangle. Brush lightly with melted butter, sprinkle with more cheese mixture, then roll lightly to press cheese into dough. Flip dough over and repeat this one more time.
Starting from a short end of the dough, use a pizza or pastry cutter to cut 1-inch thick strips; you should get about 12 strips from the sheet. Hold a strip at both ends and twist in opposite directions several times. Lay 6 twisted strips onto each baking sheet, pressing ends down onto baking sheet so twists stay in place. Brush twists with any remaining butter and sprinkle with a little more cheese mixture.
Refrigerate twists on baking sheets for at least 30 min. before baking. Preheat oven to 400 degrees while twists chill. Repeat process with second sheet of dough. (Tip: Set second batch of twists onto smaller platters to refrigerate while first batches of twists are baking.) Bake 2 sheets at a time for 10 to 15 min. until just turning golden brown. Transfer to a wire rack to cool. Repeat baking second batch of twists.