While waiting for water to boil, add the parsley, minced garlic, grated Parmesan, lemon juice, and sea salt to a food processor. Pulse until the mixture becomes coarsely chopped, then drizzle in the extra virgin olive oil while processing until you reach a chunky pesto consistency. Transfer to a bowl and stir in the mayonnaise until fully combined—this creamy pesto will be your dressing. I like to make pesto a few minutes before the potatoes finish cooking so the flavors are fresh and vibrant when combined.
Fill a large pot with water, add 1 tablespoon of salt, and bring to a boil over high heat. Cut the Yukon Gold potatoes into evenly-sized chunks (about 2-3 inches) so they cook at the same rate, then add them to the boiling water. Reduce heat to maintain a gentle boil and cook for 12-15 minutes until the potatoes are fork-tender but still hold their shape. Drain well and spread on a plate or baking sheet to cool to room temperature—this prevents the warm potatoes from breaking apart when mixed.
Once the potatoes have cooled, transfer them to a large mixing bowl and pour the pesto-mayo dressing over them. Gently fold everything together until each potato piece is evenly coated, being careful not to break them apart. Sprinkle the toasted pine nuts and freshly cracked black pepper over the top, then fold once more to incorporate. I find toasting the pine nuts yourself (just 2-3 minutes in a dry skillet) gives them so much more flavor than store-bought ones.