12 ounces raw sharp cheddar cheese, cut in 1-inch squares
1 tablespoon potato or arrowroot starch
1/4 cup warm water
Mix the fresh sourdough starter with water in a large bowl. Stir in molasses, salt, and caraway seeds. Stir in rye flour and enough of the wheat flour to make a “shaggy” dough. Turn dough out onto a smooth surface.
Knead, adding more whole wheat flour as needed, until the dough is smooth and elastic. Place in a buttered bowl, cover with a tea towel, and let rise at room temperature 4-8 hours.
Punch dough down, pour out onto a smooth surface, and divide dough into about 12 even pieces. Form each piece of dough into a disk shape, about 4 inches in diameter. Place a square of cheese in the center of the disk, then wrap the dough around the cheese and form into a smooth ball.
Place the balls of dough on a parchment-lined baking sheet. Cover with a tea towel and let rise 45 minutes to 1 hour. Meanwhile, preheat oven to 400°F (375°F for convection) and mix the potato starch with 1/4 cup water. (This will be brushed on the rolls.)
When rolls have nearly doubled in size, brush the tops with the starch water. Place the baking sheets in the hot oven. Bake for 15 minutes, turn pans 180° halfway through the baking time (to ensure they all bake evenly), and brush rolls with starch water again. Bake another 15 minutes or until nicely browned.
Remove from oven and cool on a wire rack. Don’t be surprised if some of the cheese melts out of the buns onto the baking sheet. If you like, you can scoop up the melted cheese and stuff it back into the buns where it escaped.
These are best eaten the same day they are baked, but they freeze well and can be reheated in a toaster oven to soften their cheese hearts.