Boil the potatoes, unpeeled until the point of a knife slides in with ease. Do not overcook them — you want them to keep their shape. Chill them for at least 2 hours, then peel and cut them into a fine dice.
Dice the carrots then toss them with olive oil and sprinkle them with salt. Roast them for 15 minutes in a 450ºF/220ºC oven. Let cool completely.
Plunge the frozen peas into a small saucepan of rapidly boiling, salted water. Let simmer for 1-2 minutes. Drain, then immerse in a small bowl with ice water. This will help stop them cooking and retain their brilliant bright color.
Fry the bacon lardons/pancetta until the fat is rendered. Remove to a plate covered with a paper towel to drain.
You can prepare these ingredients 1-2 days before, keeping them in the refrigerator in a non-reactive bowl covered with plastic wrap.