Preheat oven to 350°. In a medium saucepan, melt butter with honey over medium heat. Add sugar and salt and whisk until well combined. Add flour and continue to whisk until no lumps remain. Transfer to a small bowl and let cool slightly, about 5 minutes.
Line 2 flat rimmed baking sheets with parchment paper. Spoon 1 heaping tsp. honey mixture onto sheets about 4 in. apart (they will spread a lot).
Bake until dark golden brown and small holes appear throughout, 10 to 12 minutes. Keep oven on. Let cool on tray until starting to firm up, 2 to 3 minutes. While cookies cool, use a paring knife to separate any cookies that have melted together and to shape each into a circle. Working in batches of 3 or 4, carefully peel cookies off paper and lay over a rolling pin. Let cool on pin until completely crisp, about 3 minutes. If cookies firm up before you can shape them, put baking sheet back in oven to warm slightly, about 1 minute.