In a mixing bowl, combine the shredded chicken, basil pesto, and mayonnaise. Stir until well mixed. Season with salt and pepper to taste.
Preheat a skillet or grill pan over medium heat and add a drizzle of olive oil.
Slice the ciabatta rolls in half and lightly toast them on the skillet or grill until golden brown.
On the bottom half of each roll, layer a generous portion of the pesto chicken mixture, followed by fresh spinach, sliced tomatoes, and a slice of mozzarella cheese.
Place the top half of the roll on each sandwich and press down gently.
Grill the sandwiches in the skillet for about 3-4 minutes on each side, or until the cheese is melted and the bread is crispy.
Remove from heat, slice in half, and serve warm.