Preheat the oven to 375Â°F. Lightly grease an 8' square or 9' round pan.
In a large bowl, whisk together the flour, baking powder, baking soda, and salt. Add the butter, working it into the flour until the mixture is crumbly. Toss in the grated cheese. Mix the buttermilk and egg, and add to the dry ingredients, stirring just until everything is moistened.
Scoop the sticky dough into the pan, using your wet fingers to spread it to the edges of the pan. Bake the bread for 40 to 45 minutes, until a cake tester inserted into the center comes out clean. Its internal temperature at the center will be close to 200Â°F.
Remove the bread from the oven, and loosen the edges with a table knife. Wait 5 minutes, then gently turn it out onto a rack to cool. It's tempting, but wait about 20 minutes before cutting the bread, if you can; it's a bit crumbly when hot.