Heat oven to 425º F. Sprinkle a rimmed baking sheet with the cornmeal. Shape the dough into a 14-inch circle and place on the prepared baking sheet.
Brush the dough with 1 tablespoon of the oil and bake until puffed and golden, 15 to 20 minutes.
Meanwhile, in a medium bowl, toss the shallots, thyme, the remaining tablespoon of oil, and ¼ teaspoon each salt and pepper.
Top the partially cooked dough with the ham, shallot mixture, and cheese. Bake until the crust is crisp and the cheese has melted, 12 to 15 minutes.