Process the parsley with the olive oil, walnuts, parmesan cheese, garlic and a pinch of pepper in a blender until smooth to make the pesto. Taste and add salt accordingly.
To Make the Caprese Salad
Take two plates and slice the tomatoes and the mozzarella cheese into equally thick slices and alternate on each plate.
Drizzle over 2 tablespoons of the parsley walnut pesto and serve at room temperature.