Whisk the flour, baking powder, baking soda, salt, and sugar together in bowl. Rub in 2 tablespoons of butter until absorbed, and then rub in the remaining butter until mixture resembles coarse sand. Whisk the milk and sour cream into a liquid measuring cup; stir the sour cream and milk into the dry ingredients.
Turn the dough out of the bowl and knead very lightly and flatten into a square. Using a rolling pin, roll the dough into a 9 by 12-inch rectangle. Trim dough's rough edges with a pizza cutter or a knife, and then cut it in half lengthwise to make 2 rectangles. Lay 3 sausage links end to end, lengthwise, down the center of each piece of dough. Fold the dough over the sausages into long rolls with overlapping dough on the bottom. Slice each roll crosswise into 8 (1 1/2-inch) pieces.
Transfer rolls to a baking sheet. Bake until golden, about 20 minutes. Serve warm with honey mustard.
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