In the bowl of a stand mixer, add both flours, sugar, baking soda, and baking powder; mix on low speed to combine. Add butter, a little at a time, followed by salt. Continue to mix until the mixture has a “sandy” texture, about 5 minutes. Add heavy cream and crème fraîche, followed by the cheese, bacon, and chives. Continue mixing until just combined.
Place dough on a cutting board and wrap in plastic. Using a rolling pin, shape into a rectangle (about 7x9-inches) and chill for 20 minutes.
Preheat oven to 325 F. Once dough is chilled, cut it into rectangles and place on a rimmed baking sheet lined with parchment paper. Brush tops with heavy cream and add more cheese. Finish with freshly grated black pepper. Bake for 20 minutes.
Scones are done when golden brown and the cheese is melted.