Position oven rack in the center of oven; preheat oven to 400°; line a baking sheet with parchment paper.
In a bowl, stir egg and buttermilk together.
In another bowl, whisk flour, oats, sugar, baking powder, baking soda, salt, and nutmeg together.
Drop in the butter and, using your fingers, toss to coat the pieces of butter with flour.
Quickly, working with your fingers or pastry blender, cut and rub the butter into the dry ingredients until the mixture is pebbly (you will have pea-size pieces, pieces the size of oatmeal flakes, and pieces the size of everything in between—that is just right).
Pour the egg/buttermilk mixture over the dry ingredient; stir with a fork just until the dough, which will be wet and sticky, comes together; don’t overmix.
Still in the bowl, gently knead the dough by hand or turn it with a rubber spatula 8-10 times.
Turn the dough out onto a lightly floured work surface and divide it in half.
Working with one piece at a time, pat the dough into a rough circle that is about 5 inches in diameter; cut it into 6 wedges and place on baking sheet.
Bake for 20-22 minutes, or until their tops are golden and firmish.
Transfer to a rack; cool for 10 minutes before serving.
**These scones are bumpy, lumpy, and handmade looking.