Mr. Crunchy with an Egg (Mrs. Crunchy) - Alton Brown

Ingredients

• 2 tablespoons unsalted butter
• 1 ounce all-purpose flour
• 1/4 teaspoon freshly grated nutmeg
• 1/2 teaspoon kosher salt
• 1/2 teaspoon ground white pepper
• 8 fluid ounces whole milk
• 2 teaspoons fresh thyme leaves
• 4 (1/2-inch thick) slices sourdough bread
• 2 tablespoons whole-grain mustard
• 8 ounces thinly sliced Black Forest ham, cut into 1-inch wide strips
• 8 ounces Gruyere, grated
• 2 teaspoons herbes de Provence
• 2 tablespoons olive oil
• 4 large eggs
• Kosher salt
• Freshly ground black pepper