Heat the oven to 425°F (220°C) and line a baking sheet with parchment. A fully preheated oven is important because the cold butter needs immediate high heat to create steam and help the biscuits rise.

Whisk the flour, baking powder, baking soda, salt, and optional sugar together in a large bowl. Mixing the dry ingredients first distributes the leaveners evenly throughout the dough.

Add the cold cubed butter and cut it in with a pastry cutter or your fingertips until coarse crumbs form, leaving some pea-sized pieces visible. Those small butter pieces create flaky pockets as they melt in the oven.

Stir in the finely minced jalapeño and the shredded cheddar if using. Toss gently so the pepper and cheese are coated with flour rather than clumping together.

Pour in the cold buttermilk and mix gently just until a shaggy dough forms. If dry flour remains at the bottom, add extra buttermilk 1 tablespoon at a time, stopping as soon as the dough comes together.

Turn the dough onto a lightly floured surface and pat or gently fold it 3 to 4 times. Flatten it to about 3/4-inch thickness while handling it as little as possible.

Cut rounds with a 2 1/2- to 3-inch biscuit cutter, pressing straight down without twisting. Twisting can seal the edges and keep the biscuits from rising evenly.

Arrange the rounds close together for softer sides or about 1 inch apart for crisper edges. If the butter has softened during shaping, chill the unbaked biscuits for 10 minutes.

Bake for 12 to 16 minutes, until the biscuits are well risen and golden on top. Watch the final minutes closely because oven temperatures and biscuit thickness can affect browning.

Brush the hot tops with melted butter if desired and serve warm. Letting them rest for just a minute or two makes them easier to split while keeping the centers tender.