In a large bowl, combine the flour, baking powder, granulated sugar, salt, and baking soda.
Preheat oven to 425˚F (220˚C). Line a large rimmed baking sheet with parchment or lightly grease.
Cut the butter into the flour using a dough blade, your fingers, or forks until the mixture becomes coarse and no pieces are larger than a pea.
Mix in the cheddar cheese and sun-dried tomatoes.
Fold in the buttermilk until just combined. Knead lightly to bring the dough together, but don’t overwork. If too dry, add a little more buttermilk.
On a lightly floured surface, gently roll the dough into a rectangle about 3/4 inch (2 centimeters) thick.
Fold the dough into thirds like a letter- short side folded over the center, then the other short side folded on top in the center to create three layers.
Rotate the dough 90 degrees, then gently roll out/flatten it again into a 3/4 inch (2 centimeter) thick rectangle and repeat the folding into thirds one more time.
Rotate the dough again and roll into a sheet about 3/4 inch (2 centimeters) thick.
Use a 2 1/2 inch (6 centimeter) round biscuit cutter to cut out circles of dough. Do not twist the cutter. Transfer the rounds to the prepared baking sheet about 1-2 inches (2.5-5 centimeters) apart.
Lightly brush the top of each biscuit with additional buttermilk and bake in the preheated oven until golden and flaky, about 15 minutes.
Serve the Cheddar Sun-Dried Tomato Biscuits warm from the oven with butter, slices of cheese/cured meat, or as a the base for a sandwich.