Heat the oven to 375°F. In a bowl, combine the Baking Mix, the thyme, and 1/2 cup of the cheese. Break the egg into the buttermilk and stir briefly with a fork to combine. Make a shallow well in the dry mix and pour in the buttermilk. With as few strokes as possible, stir until the mixture is just combined. It should be loose, but if it doesn’t hold together at all, add more buttermilk 1 Tbs. at a time.
Generously flour a counter and turn the dough out onto it; it will be shaggy and very soft. Scrape any bits in the bowl onto the mound of dough. Flour your hands. Shape the mixture into a very loose rectangle with the short side nearest you. Using a bench knife, a pastry scraper, or a spatula to help lift the ragged dough, fold the bottom third over the center third, and then the top third over the center, as if folding a business letter. Pat down to shape another rectangle, turn it so the short side is nearest you, and repeat the folding. Pat down again into more of a square shape, 3/4 inch thick and about 8-1/2 inches square. With a pastry brush, brush off any excess flour. Punch out the biscuits with 2-1/2-inch round cutter. Gather the scraps, press them together lightly, and punch out more biscuits until all the dough is used. Bake on an ungreased baking sheet (or one lined with parchment) for 15 minutes. Pull out the oven rack, quickly sprinkle the biscuits with the remaining cheese, and continue baking until lightly browned on top, about 10 minutes.
If you want plain biscuits, just leave out the cheese and thyme.