Cook the potatoes:

• Boil cut potatoes in salted boiling water until they easily fall from a knife pierced into them. Allow to cool, then dice and place in a large bowl.

Cook the eggs:

• Bring a medium pot of water to a boil (large enough to accommodate all the eggs in a single layer). As soon as the water boils, gently add the eggs. Set a timer for 9 minutes. Bring back to a boil and then turn down to a simmer. Meanwhile set up a bowl of ice water, large enough to accommodate all the eggs. When the eggs are done, use a slotted spoon to immediately transfer the eggs to the bowl of ice water. Peel and chop when cool enough to handle.

Cook the macaroni:

• Bring a large pot of water to a boil. Add salt. Cook macaroni according to package instructions, drain, then rinse with cold water and set aside.

Make the sauce:

• In a small bowl mix together the sauce ingredients. Add the onion, eggs, carrots, peas, and macaroni to the bowl with the potatoes. Mix in dressing until thoroughly combined. Check seasonings.

• Coat prepared vegetables with olive oil, then season with salt and pepper. Grill vegetables slices, whole asparagus, and whole tomatoes until desired doneness. Chop into 1-inch pieces and set aside.
• To make the pesto, wash and dry basil thoroughly. Place basil, pine nuts, chopped garlic, and salt in the work bowl of a food processor. Process quickly to make a coarse paste. With the motor running add the olive oil, and process for another 5 seconds. Place pesto in a medium bowl and mix in the cheeses. Mix in butter if using. If pesto is too thick add a bit more olive oil. Taste and correct for salt.
• Put the desired amount of pesto in a large bowl (enough to accommodate all the pasta and vegetables, plus room for tossing). Add the cooked pasta, toss thoroughly, adding more pesto to taste. Add diced grilled vegetables, gently toss again. Adjust seasonings. Top with additional parmesan cheese if desired. Serve warm or at room temperature.