Place potatoes in a large pot and pour in water to cover by 2”. Season with salt and bring to a boil. Reduce heat and simmer until a paring knife easily slides at least ½” into potatoes, 25–30 minutes. Drain; return potatoes to pot. Let cool slightly, then mash with a potato masher or fork until smooth. Set aside.

Cook Swiss chard and peas in a medium pot of boiling salted water until chard is tender and peas are bright green, about 2 minutes. Using a slotted spoon, transfer chard and peas to a colander set in a bowl of ice water; let sit until cold. Drain, then squeeze out as much liquid as possible from chard. Transfer chard and peas to a cutting board and coarsely chop; set aside.

Preheat oven to 400°. Thinly slice mortadella; set aside.

Whisk ricotta, Parmesan, eggs, garlic, nutmeg, 1 tsp. salt, and several grinds of black pepper in a medium bowl until combined. Transfer to a small resealable plastic bag.

Fold 2 kitchen towels so they each fit snugly inside a large baking dish. If lasagna noodles are crimped together, you can separate them. Spread a thin layer of mashed potatoes over bottom of each baking dish (it should be about ¼” thick; you won’t use all of mashed potatoes). Arrange 3 noodles, slightly overlapping, on top to form a single layer, trimming to fit. Spread half of ricotta mixture over, pushing it into crevices and out to edges with an offset spatula or spoon. Top with a third of chard mixture, then a layer of mortadella (use half of it where you’re using half the chard, and the other half where you’re using the full amount).

Repeat layers of noodles, ricotta mixture, chard mixture, and mortadella 3 more times.

Arrange another layer of noodles over each lasagna, then spread remaining ricotta mixture over, pushing it into crevices and out to edges. Top with a final third of chard mixture and a layer of mortadella. Evenly ladle cream over each lasagna. Sprinkle Gruyère over, pressing gently so it adheres; season with salt, then pepper.

Cover lasagna with a lightly oiled piece of foil and place on a foil-lined baking sheet (to catch any spills). Bake until bubbling gently on top and heated through, 45–50 minutes. Remove foil and increase oven temperature to broil. Broil until cheese is browned and bubbling and edges are crisped, about 5 minutes. Let sit 10 minutes.

Do Ahead: Lasagan can be assembled 1 day ahead. Cover and chill. Increase final bake time by 10–15 minutes.