Set your oven to 425°F (220°C) and prepare a baking sheet by lining it with parchment paper or lightly greasing it.
In a large mixing bowl, sift together the all-purpose flour, granulated sugar, baking powder, sea salt, and baking soda to evenly distribute the ingredients.
Use a pastry cutter or two forks to cut the cold butter (half of the 1/2 cup) and cold butter-flavored vegetable shortening into the dry ingredients until pea-sized lumps form.
Pour the cold buttermilk into the flour mixture and stir gently with a spoon or spatula until just combined; the dough will be slightly sticky and shaggy.
Turn the dough onto a lightly floured surface and fold it over itself 3–4 times to build layers, then pat into a thick rectangle about 1 to 1 1/2 inches tall.
Using a large biscuit cutter or sturdy glass, cut out rounds about 3 1/2 to 4 inches in diameter without twisting to keep edges sharp.
Place biscuit rounds on the prepared baking sheet about 1 to 2 inches apart and bake for 15–18 minutes until golden brown.
Brush the hot biscuits generously with melted butter for a rich, glossy finish.
Transfer biscuits to a wire rack to cool slightly before serving warm with your favorite accompaniments.