Combine cheese, thyme, sage, and pepper in a small bowl.
Roll out dough on a lightly floured work surface until a bout 1/8 inch thin.
Sprinkle 1/3 of cheese mixture over half the dough, then fold the un-cheesed half over the cheesed. Roll out again until dough is 1/8 inch thin. Repeat 2 more times.
Transfer dough to a baking sheet and chill in the refrigerator for 30 minutes.
Prepare the oven by positioning one rack near the top third of the oven, and the other near the bottom third. Prepare 2 large baking sheets by lining with parchment paper. Preheat oven to 425 F.
Using a pizza cutter, cut pastry in half length-wise. Cutting perpendicularly, cut the dough into 1/2 inch wide strips.
Twist each strip a few times and transfer to baking sheets, leaving 1/2 - 3/4 inch empty space between.
Whisk together egg and water, then brush onto twists. Sprinkle on coarse salt and pepper.
Bake twists with one pan at the top of the oven, and the other at the bottom, for 5 minutes, then switch. Bake another 5 minutes, until golden brown.
Remove from oven and let twists cook on baking sheets.
Can be made one day ahead. Cover cooled twists with foil and store at room temperature.
Notes
You can substitute crescent roll or flaky biscuit dough for puff pastry for a similar texture.