Pre-heat the oven to 400°F with 2 racks set in the middle position.
In an electric stand mixer fitted with the paddle attachment, combine the salt, baking soda, baking powder, sugar, and flour. Mix on low until combined. Add the butter and cover the top of the bowl with a large kitchen towel and mix on medium speed until the butter breaks up in to smaller pieces throughout the flour mixture (the towel helps the flour and butter from going all over your kitchen counters!). Add the cherries and dark chocolate chunks or chips and mix on low speed until combined. Pour in the buttermilk and heavy cream and mix on medium speed until just combined. Do not overmix or the scones will be tough!
Use a medium ice cream scoop (about 2 ounces) and drop leveled scoops of the dough on to 2 large baking sheets lined with parchment paper. Bake in the oven for 8 minutes then rotate the baking sheets top to bottom and front to back. Bake until the scones are light golden brown and just cooked through, about 8 additional minutes.
Cool for at least 5 minutes on the baking sheet before serving the scones warm.