Heat a dry small nonstick skillet over medium heat.
Place 1 slice of bread, butter side down, in the pan and spread 1 tablespoon of basil pesto evenly over it. Then, top with provolone cheese and then the diced tomato.
Spread 1 tablespoon of butter evenly over one side of each slice of sourdough bread.
Place one slice of bread, butter-side down, into the preheated skillet. Spread 1 tablespoon of basil pesto evenly over the bread, then layer with the provolone cheese and diced tomato.
Spread the remaining tablespoon of pesto on the unbuttered side of the second slice of bread, then place it pesto-side down over the tomatoes with the buttered side facing up.
Cook for about 2 to 3 minutes, or until the bottom is golden brown and crispy.
Carefully flip the sandwich with a wide spatula, gently pressing down to help the cheese melt evenly.
Cook for another 2 to 3 minutes, or until the second side is golden brown and the cheese is completely melted.
Remove from the skillet, let the sandwich rest for 1 to 2 minutes, then slice and serve warm.