Preheat oven to 375°. Position one oven rack in bottom third of oven. Position second oven rack 6 inches below broiler. Spray a 3-quart straight-sided enameled cast-iron Dutch oven with cooking spray. Sprinkle with 3 tablespoons Parmesan to coat.
In a 10-inch cast-iron skillet, melt butter over medium heat until bubbly. Whisk in flour until smooth; cook, whisking constantly, for 2 minutes. Whisk in salt, mustard, red pepper, and white pepper. Gradually whisk in milk until smooth. Cook, whisking frequently, until sauce is thickened and bubbly, 5 to 7 minutes.
Remove skillet from heat. Gradually whisk in Gruyère and remaining 5 tablespoons Parmesan until melted and smooth. Transfer cheese sauce to a large bowl. Whisk in egg yolks, one at a time, until well combined. Stir in ham and thyme.
In a large bowl, beat egg whites and cream of tartar with a mixer at high speed until medium peaks form. Gently fold one-third of egg whites into cheese sauce. Repeat process twice with remaining egg whites. Gently spoon mixture into prepared Dutch oven, spreading top smooth and leaving at least 1 inch of headspace at top of pot. Wipe inside rim of pot clean.
Bake until puffed and golden brown, about 40 minutes, placing a piece of foil on broiler rack after 30 minutes to prevent excess browning. Serve immediately.
Recipe by Southern Cast Iron at https://southerncastiron.com/country-ham-and-cheese-souffle/