Preheat oven to 350 degrees F. Line a baking sheet with parchment paper.
Using a stand mixer fitted with the paddle attachment (or hand mixer), mix together the flour, baking powder, baking soda, and salt. Mix on low speed until combined. Add in the pieces of cold butter and beat on medium-low speed for about 2 minutes, or until the mixture resembles coarse crumbs. Add in the grated cheese and mix just until combined, about 30 seconds.
In a small bowl, whisk together the buttermilk, heavy cream, egg, and jalapeño until well combined. With the mixer running on low speed, pour the mixture into the flour mixture and beat for about 15 seconds or until the dough just comes together. There will still be loose flour at the bottom of the bowl. Gather the dough into a ball and keep turning it over in the bowl to until you have gathered all of the loose flour and it is mixed in.
On a lightly floured work surface, pat the dough into a 1-inch thick layer. Using a 3-inch biscuit or cookie cutter, cut out the biscuits and place them on the cookie sheet. Gently bring together the loose scraps and cut out more biscuits. Repeat until all the dough is used up. You will have about 8 biscuits.
Brush the tops of the biscuits with the remaining 1 tablespoon of heavy cream, and bake for about 40 to 45 minutes, or until the biscuits are golden brown. Cool on the cookie sheet on a wire rack.
Serve slightly warm.