In a light-colored medium saucepan, melt butter over medium heat. Add sage; cook, stirring frequently, until butter is fragrant and a deep amber color, 8 to 10 minutes. Pour into a shallow baking dish, and let cool for 10 to 15 minutes. Freeze until solid, about 30 minutes.
Preheat oven to 400°F (200°C). Line 2 baking sheets with parchment paper.
In the work bowl of a food processor, pulse flour, sweet potato, sugar, baking powder, kosher salt, and baking soda until combined.
Cut frozen butter into 1-inch pieces; add to flour mixture, and pulse just until butter pieces are the size of small peas and mixture is crumbly. Add cold buttermilk, and pulse until a shaggy dough forms.
Turn out dough onto a lightly floured surface. Pat dough into a rectangle about 1 inch thick. Cut dough into fourths. Stack fourths on top of each other, and pat into a rectangle. Repeat procedure 3 more times. Pat or roll dough to ¾-inch thickness.
Using a 2½-inch round cutter dipped in flour, cut dough without twisting cutter, rerolling scraps as necessary. (To reroll scraps, stack pieces on top of each other, and pat to ¾-inch thickness.) Place 2 inches apart on prepared pan. Freeze until cold, about 10 minutes.
In a small bowl, whisk together egg and 1 tablespoon (15 grams) water; brush onto biscuits, and sprinkle with sea salt.
Bake until golden brown, 15 to 18 minutes, covering with foil after 10 minutes of baking to prevent excess browning. Serve with softened butter.