Fill up a medium or large saucepan with the potatoes and add enough water to cover them. Place over medium-high heat and bring the potatoes to a boil. Once boiling, reduce the heat to and simmer the potatoes until they are just tender, about 14-16 minutes. Use a slotted spoon to transfer the potatoes to a cutting board to allow to cool slightly. Reserve 1-2 inches of the cooking water and drain the rest. Prepare an ice bath (a large bowl of water with ice).
Trim the asparagus of its woody, bitter ends. I like to snap them below their natural snap point to waste less of the vegetable. Bring the water back to a boil and place a collapsible steamer inside the saucepan (make sure it fits the saucepan you’re using). Place the asparagus in the steamer basket, cover, and steam until crisp-tender, about 4 to 5 minutes. Transfer the cooked asparagus to the ice bath to prevent them from overcooking. Drain the asparagus.
While the potatoes and asparagus are cooking, prepare the rest of the vegetables. Use a wide Y-shaped vegetable peeler to shave the carrots into ribbons. Thinly slice the radishes and the avocado. Add the carrot ribbons, radish slices, avocado, and fresh mint leaves to the salad greens.
To make the pesto (I make it while the potatoes are cooking), place all of the ingredients except for the extra virgin olive oil in a food processor and blend until a paste starts to form. With the motor running, drizzle in the olive oil until a creamy, smooth texture comes together. It should be slightly thicker and creamier and less oily than traditional pesto. If you want it a little thinner, you can add a spoon or two of water (or more olive oil).
Toss the cooked potatoes and asparagus with the pesto until well-coated (you will have leftover pesto). Serve the pesto potato-asparagus salad on top of the salad green mixture and serve. Store the remaining pesto in a airtight glass jar in the fridge for 5-6 days.