Line a rimmed baking sheet with parchment paper.
In a medium skillet, melt softened butter over medium-high heat. Add celery and onion; cook, stirring frequently, until tender and fragrant, 5 to 6 minutes. Remove from heat; let cool completely.
In a large bowl, whisk together flour, kosher salt, baking powder, sugar, poultry seasoning, garlic powder, and pepper. Add cold butter, tossing to coat. Using a pastry blender or your hands, cut in butter until mixture is crumbly and butter pieces are pea-size. Stir in cooled vegetable mixture and cheese. Add cold buttermilk; stir with a fork until a shaggy dough forms. (Do not overmix.)
Turn out dough onto a lightly floured surface. (Dough will be crumbly and almost dry.) Pat dough into a square about 1¼ inches thick. Using a bench scraper or sharp knife, cut into fourths. Stack fourths on top of each other, and pat down to 1¼- inch thickness. Repeat cutting and stacking 3 more times. (Dough may seem too shaggy at first but will come together and be easier to work with as you go.)
Roll dough into a 1¼-inch-thick square. Using a 2¼-inch round cutter dipped in flour, cut 12 rounds from dough, rerolling scraps once. Place 1 inch apart on prepared pan. Freeze for 15 minutes.
Preheat oven to 425°F (220°C).
In a small bowl, whisk together egg and 1 tablespoon (15 grams) water; brush onto biscuits. Sprinkle with sea salt.
Bake until golden brown, 18 to 22 minutes. Let cool on pan for 5 minutes. Best served warm. Store in an airtight container for up to 3 days.