Preheat oven to 500 degrees F.

In a food processor, blend flour, baking powder, baking soda, salt, and pepper briefly (about 3 pulses). Add butter and process to a "mealy" consistency. Add herbs, cheese, and roasted red peppers, processing briefly to combine. Transfer mixture into a large bowl, add 1 cup buttermilk and stir to moisten. If needed, add more buttermilk, up to 1/4 cup.

Place dough on a floured surface and form into a disk, 3/4 to 1-inch in thickness. Cut into wedges, brush top of each wedge with egg wash. Place on a cookie sheet and bake for approximately 15 to 20 minutes. Place on rack and let cool to room temperature.