Preheat the oven to 350 degrees F. Line two sheet pans with parchment.
In a large mixing bowl, whisk together the flour, sugar, baking powder, salt and cayenne. Add the butter and toss gently to coat. Work the butter into the flour with the tips of your fingers until the mixture resembles rough cornmeal with pea-size bits of butter scattered throughout. Stir in the ham and cheese to evenly distribute.
Whisk together the buttermilk and egg and add it to the butter-flour mixture; stir with a wooden spoon to distribute the moisture. Use your hands to gently bring the dough together, being careful not to overwork the dough.
Drop 1/4-cup mounds of dough, spaced a few inches apart, onto the prepared pans. Bake until golden brown and the scones spring back when gently poked, 15 to 20 minutes.