In a high-speed blender, add the basil, walnuts, vinegar, mustard, garlic, salt, pepper, and oil. Blend on low, slowly increasing to high until mostly smooth.
Toast your bread or, if it’s a really fresh hearty loaf , leave it untoasted. Toasting the bread will make it hold the sandwich together better.
Spread the basil spread on one side of each slice of bread. Top one slice with slightly mashed avocado, then mozzarella, cucumber slices, and lettuce or arugula (if using). Top with the other slice of bread and carefully cut in half.