Place potatoes in a large pot and cover with cold water by 2 inches. Bring potatoes to a boil over medium high heat. Reduce heat to medium and cook potatoes until they are just cooked through, about 15 - 20 minutes. Using tongs, remove potatoes, drain thoroughly and let cool slightly. Cut cooled potatoes into 1/2-inch cubes and set aside.
While the potatoes are cooling, bring the water back to a boil and add carrots and peas and cook until vegetables are al dente, about 5 - 7 minutes. Drain vegetables and let cool to room temperature.
In a large bowl, combine the tuna, mayonnaise with the reserved potatoes and vegetables. Gently fold in the eggs and season with salt and pepper to taste. Serve on a bed of butter lettuce cool or at room temperature.