Bring salted water to a boil in a medium saucepan. One vegetable at a time, cook the carrots, potatoes, and green peas until tender: 3 to 4 minutes for the carrots, 4 to 5 minutes for the potatoes, 1 to 2 minutes for the peas. As you move on, remove with a slotted spoon and place in a large bowl. When it has cooled, incorporate the nopalitos.
Whisk the vinaigrette well. Toss the lettuce with some of it and set aside. Mix the shredded chicken with some of it and set aside. Toss the cooked vegetables with some of it and set aside.
In a large platter, spoon the lettuce as the bottom layer, arrange the chicken in the middle, and the vegetables on the sides. Garnish with radishes, avocado and in the corners, add the pickled jalapeños and chipotles in adobo. You can drizzle any remaining vinaigrette over the top. Serve with warm corn tortillas and your guests can eat the salad on its own, or tuck parts of it into tacos! I add avocado, mash it, top with chicken and veggies and top with both, pickled jalapeños and chipotles.