Put the potatoes into a large pot, cover them with cold water, and add a large pinch of salt. If they're large, cut them in half. Bring to a boil and simmer until the potatoes are fork tender, 20 to 30 minutes. Drain. Stick a fork into the potatoes, 1 at a time, lift them out of the colander and peel with a paring knife. Toss the potatoes into a bowl and roughly crush them. Drizzle with olive oil and season with salt and pepper.
Heat 2 tablespoons olive oil with the butter in a medium saucepan over medium heat until the butter melts. Add the pearl onions, sugar, and lemon juice and cook, stirring frequently, until the onions are browned, 5 to 6 minutes. Add the lemon slices, peas, and lemon zest and continue cooking until the peas are hot. Season with salt and pepper. Dump the vegetables over the potatoes in the bowl, drizzle with extra-virgin olive oil add the parsley and dill and taste for salt and pepper. Scatter the watercress over the top, fold it in just until it wilts and call it a day.