Preheat oven to 450°.
Combine first 5 ingredients, stirring with a whisk.
Heat oil in a large cast-iron skillet over medium-high heat. Add potatoes; sauté 5 minutes. Stir in ham; sauté 1 minute. Stir in egg mixture. Bake at 450° for 12 minutes or until set. Cover and let stand 10 minutes. Cut into 8 wedges.