Place eggs in a medium pot covered with water. Bring to a steady boil. Cover and turn off heat and let sit for 14 minutes. Drain and rinse eggs under cold water. Peel and chop eggs and place in a medium bowl.
In a food process add basil leaves, walnuts, Parmesan cheese and garlic. Blend until mixture balls up and forms a paste. Add to bowl with eggs. Add in mayonnaise and stir until combined.
Serve on ciabatta rolls or desired bread of choice with fresh tomato slices and cheese.