savory, herbed grilled cheese french toast

Ingredients

• 8 slices french bread or sourdough bread, thickly sliced
• BATTER
• 1/2 cup buttermilk
• 2 - eggs, at room temperature & well beaten
• 1 teaspoon kosher salt
• 1/2 teaspoon thyme, leaves, minced
• 1/2 teaspoon oregano, dried
• 1/4 teaspoon white pepper
• 1 pinch cayenne pepper
• FILLING
• 1/2 to 3/4 cups sharp cheddar, finely grated
• 1/4 to 1/2 cup fontina cheese, finely grated
• 3 tablespoons parmigiano-reggiano, grated
• 2 tablespoons butter, unsalted at room temperature