Preheat the oven to 450°F. In a large bowl, whisk together the flour, baking powder, baking soda, and salt.

Add the cold, cubed butter to the flour mixture. Use a pastry cutter or your fingers to mix until the mixture resembles coarse crumbs.

Pour in the buttermilk and stir until just combined. Do not overmix.

Turn the dough out onto a floured surface and gently knead it a few times until it comes together. Pat the dough into a 1-inch thick round.

Use a biscuit cutter to cut out biscuits and place them on a baking sheet lined with parchment paper. Gather any scraps, re-roll, and cut out additional biscuits.

Bake the biscuits in the preheated oven for 12-15 minutes or until golden brown.

While the biscuits are baking, heat the olive oil in a large skillet over medium heat. Add the chorizo and cook until browned and cooked through, about 5-7 minutes.

Sprinkle the flour over the chorizo and stir to combine. Gradually whisk in the milk, stirring constantly until the gravy thickens, about 5 minutes. Season with salt and pepper to taste.

Once the biscuits are done, remove them from the oven and serve warm, topped with the chorizo gravy. Garnish with chopped parsley if desired.