Preheat oven to 450F degrees and adjust the oven rack to the middle position. Line a baking sheet with parchment paper or silicone baking mat. You can also use a cast iron skillet to bake the biscuits.
In a large bowl, add the flour, baking powder, baking soda, and salt. Using a wooden spoon, stir to combine and set aside.
Using a box cheese grater, grate the butter onto a piece of parchment paper. If you have a small piece remaining that is too small to grate (don't grate your fingers!), use a knife to cut into small pieces.
Add the butter, Chorizo crumbles, and grated cheese to the flour mixture and mix until just combined. The mixture will resemble coarse crumbs. Note: using a pastry cutter to cut the butter into the flour will also work.
Add the buttermilk and honey. Mix the dough gently until all ingredients are just combined. Don't overwork the dough.
Turn the dough out onto a lightly floured work surface, and using your hands, gently work the dough together and form into a rough rectangle. If the dough is sticky, lightly flour the top of the dough.
Once the dough has come together, fold the dough in half and with your hands, gently flatten the layers. Rotate the dough 90 degrees and fold in half again, gently flattening the layers again. Repeat this step 5 more times. Keep the surface lightly floured as needed to avoid the dough sticking to your work surface. This process is called laminating the dough which gives you all the flaky layers.
Using your hands, gently flatten the dough to 1/2 inch thick. Lightly flour a 3-inch biscuit cutter. Starting in one of the corners of the dough, gently press the biscuit cutter straight down. Repeat, making close cuts to get as many biscuits as you can before having to re-work the dough. Place the biscuits next to each other, so they are touching, on the prepared baking sheet.
Re-work any leftover dough following the folding and flattening technique above - until you get about 6 - 8 biscuits. Do not re-work the dough more than twice, otherwise, you will get a tough biscuit.
With a pastry brush, brush the reserved buttermilk on top of each biscuit. Place the biscuits on the baking pan so they are just touching.
Bake the biscuits until the tops are golden brown, about 15 minutes. Remove from the oven and serve warm. You can also brush on some melted butter before serving. Enjoy!