Sift the flour, baking powder, sugar, salt, and cayenne pepper into a food processor and pulse to combine. Add the butter and pulse 5 or 6 times until mixture resembles coarse crumbs.
Return dough to bowl, add the buttermilk and the chiles and stir with a fork until the mixture forms a ball.
Turn the dough out onto a well-floured surface and pat it down into a rough rectangle, about an inch thick. Food it over and gently pat it down again. Repeat. Cover the dough loosely with a kitchen towel and allow it to rest for 30 minutes.
Gently pat out the dough some more, so that the rectangle is roughly 10 inches by 6 inches. Cut dough into biscuits using a floured glass or biscuit cutter. Do not twist cutter when cutting; this crimps the edges of the biscuit and impedes its rise.
Place on a parchment-lined baking sheet. Bake at 425 degrees for 10 to 12 minutes or until golden brown. Remove to a wire rack to cool.
For the Jalapeño Cheese:
Combine the pimento cheese and jalapeño chiles in a bowl and mix well. Chill, covered, for 30 minutes or for up to 1 day.
Arrange biscuits on a plate and serve with jalapeño cheese.