Heat the olive oil in a 12-inch (30 cm) cast-iron skillet over medium-low heat. Add the garlic and cook for about 1 minute, until the garlic starts to soften but not brown. Add the oregano and parsley and cook for about 30 seconds more, until fragrant. Add the Swiss chard and salt and cook until the chard wilts, 2–3 minutes. Remove from skillet and set aside. Wipe out the pan.
2. Step
Make the béchamel: Melt the butter in the same skillet over medium-low heat. Add the garlic to the pan and cook until softened and fragrant, but not browned, about 1 minute. Add the flour and cook, whisking constantly, for about 2 minutes, until the mixture bubbles but has not yet started to brown.
3. Step
Slowly stream in the warm milk, starting with just a few splashes, whisking constantly. The mixture will be very clumpy at first, but will eventually come together as a thin sauce. Cook until the mixture begins to simmer, and then reduce the heat to low and cook, still stirring frequently, until the sauce thickens enough to coat the back of a spoon, about 10 minutes. Add the salt, pepper, cayenne, and nutmeg and whisk to incorporate. Pour the béchamel into a liquid measuring cup, but do not scrape out the pan. You want a thin coating of sauce left in the bottom of the skillet.
4. Step
Assemble the lasagna: Add the olive oil to the pan and whisk into the béchamel.
5. Step
Pour warm water into a glass baking dish. Dip each lasagna noodle in the warm water for a few seconds, then lay in the skillet, breaking as needed to fit. Once you have a single layer at the bottom of the pan, top with ⅓ of the béchamel, ⅓ of the frozen peas, ⅓ of the sautéed Swiss chard, ⅓ of the mozzarella, and ⅓ of the Parmesan. Repeat to make 2 more layers with the remaining ingredients.
6. Step
Cover the skillet with 2–3 layers of foil and seal tightly to ensure no steam escapes.
7. Step
Cook the lasagna over medium-low heat for 30–45 minutes, until a toothpick slides easily through the noodles.
8. Step
Uncover the lasagna and top with the basil. Serve immediately.
