Preheat oven to 375°. In a medium saucepan, bring butter, salt, and 1 1/2 cups water to a boil over medium-high heat. Add flour and stir constantly until dough comes together and pulls away from pan, 1 to 1 1/2 minutes. Remove from heat; let cool 2 minutes.
Add eggs one at a time, stirring vigorously after each addition until eggs are incorporated and dough is glossy. Stir in 1 1/4 cups cheese. In a small bowl, combine herbs, then stir 1 1/2 tbsp. into dough.
Line 3 rimmed baking sheets with parchment paper. Spoon dough onto sheets by 4-tsp. portions (measure the first portion, then eyeball the rest) about 1 in. apart. Combine remaining cheese and herbs, then sprinkle onto dough.
Bake 1 or 2 sheets at a time (for 2, switch sheet positions halfway through baking) until puffs are deep golden, 35 minutes. With a small knife, poke each puff at the "waist" to release steam. Bake until crisp and richly browned, 5 to 8 minutes more. Serve warm.
*For an accurate measurement, whirl chunks with the metal blade or grate with the smallest holes on a hand grater; don't shred.
Make ahead: Through step 3, up to 1 day, chilled airtight, or 1 month, frozen. (Freeze until solid, transfer to bags, and bake frozen.)