Preheat the oven to 425°F with a rack in the middle to upper third. Line a baking sheet with parchment and flour it generously.
In a medium bowl, whisk together the flour, salt, baking powder, and sugar.
Work the butter into the flour until the mixture is unevenly crumbly, with some of the butter remaining in larger pieces.
Mix in the cheese, chives or scallion tops, and bacon until evenly distributed.
Add the starter, stirring to combine; depending on the liquidity of your starter, the mixture will be crumbly or will start to come together in large-ish clumps.
Pour the cream into a spouted measuring cup. Drizzle in the cream, adding just enough for the dough to become cohesive.
Transfer the shaggy dough to the prepared baking sheet.
Divide the dough in half, and pat each half into a disk about 5" wide and ¾" to 1" tall.
Use a knife to cut the disks into six wedges each, spreading the wedges apart on the pan.
Brush the scones with a bit of cream or milk.
Bake the scones for 22 to 24 minutes, until they're a light-to-medium golden brown.
Remove the scones from the oven, and cool them briefly right on the pan. Serve warm or at room temperature.
