In large shallow dish, lightly whisk together eggs, milk, thyme, pepper and salt; set aside. Spread 4 of the bread slices with prepared pesto; top with sliced cheese and tomato. Sandwich with remaining bread. Dip into egg mixture, turning to coat both sides and soak up liquid.
Make-ahead: Cover and refrigerate on waxed paper-lined rimmed baking sheet for up to 12 hours. In large nonstick skillet, melt butter over medium heat; fry sandwiches, turning once, until golden and cheese is melted, 6 minutes.
Makes 4 servings