Preheat oven to 425°F (220°C). Line a baking sheet with parchment paper.

In a large bowl, whisk together flour, sugar, baking powder, salt, onion, pepper, and baking soda. Add cold butter, and toss to coat. Using a pastry blender or 2 forks, cut in butter until mixture is crumbly and butter is pea-size. Stir in 1 cup (113 grams) cheese. Add cold buttermilk, and stir with a fork until a shaggy dough forms.

Turn out dough onto a lightly floured surface, and pat into a 9-inch square (about 1 inch thick). (Dough will be crumbly.) Using a bench scraper, cut dough in quarters. Stack quarters, and pat or roll into a 9-inch square. Repeat procedure twice. Using a knife or bench scraper dipped in flour, cut dough into 16 (2¼-inch) squares. Place at least ½ inch apart on prepared pan. Freeze for 15 minutes.

Brush tops of dough with melted butter, and sprinkle with remaining ⅓ cup (38 grams) cheese.

Bake until golden brown, 16 to 18 minutes. Serve hot.