Soak cedar planks in water for at least 4 hours or overnight. Drain and pat dry.
Remove the centers of each slice of bread with a 3-inch round cookie cutter. Beat 3 of the eggs with milk and 2 tablespoons of the Applewood Rub in medium bowl until well blended.
Lightly oil 1 side of each of the planks. Place planks, oil side up, on preheated grill over medium heat. Dip bread in egg mixture. Place on planks. Break an egg into each of the holes. Sprinkle eggs with remaining 1/2 teaspoon Applewood Rub. Cover grill.
Grill 10 minutes. Sprinkle eggs with cheese and additional Applewood Rub, if desired. Grill, covered, 10 minutes longer.