Lightly brush one side of each bread slice with olive oil or spread with softened butter.
On the non-oiled side of two bread slices, spread a thin layer of pesto sauce. Place the sliced turkey evenly on top of the pesto. Add the mozzarella cheese slices on top of the turkey. Layer on the tomato and avocado slices next, followed by a handful of fresh spinach or arugula. Spread a thin layer of mayonnaise on the non-oiled side of the remaining two bread slices before placing them on top to close the sandwich.
Heat a skillet or panini press over medium heat. Place the sandwiches in the skillet (or in the panini press) and cook for about 3–4 minutes on each side until the bread is golden brown and the cheese has melted.
Once grilled to perfection, remove the sandwiches from the skillet or press and let them cool for about a minute before slicing them in half.
Serve your warm Turkey Pesto Sandwiches alongside chips, salad, or pickles.