Bring a large pot of salted water to a rolling boil. Add the spaghetti or linguine and cook according to package directions until al dente. Before draining, reserve about 1 cup of the starchy pasta water. Drain the pasta and set aside.

While the pasta cooks, heat the olive oil in a large skillet or Dutch oven over medium heat. Add the diced shallot (or onion) and cook for 2-3 minutes until softened and translucent.

Add the minced garlic and red pepper flakes to the skillet. Sauté for 1 minute until fragrant, being careful not to burn the garlic. Add the chopped Swiss chard stems first, cook for 2 minutes, then add the chopped chard leaves and cook until wilted, about 3-5 minutes. Season lightly with salt and pepper.

Add the drained pasta directly to the skillet with the Swiss chard mixture. Pour in the lemon juice, add the lemon zest, and half of the reserved pasta water. Toss vigorously to combine, allowing the pasta water, lemon, and olive oil to emulsify and create a light sauce. If the sauce seems too thick, add a little more pasta water, a tablespoon at a time, until desired consistency is reached.

Stir in the grated Parmesan cheese until melted and fully incorporated into the sauce. Taste and adjust seasoning with additional salt, pepper, or lemon juice if needed. Serve immediately, garnished with extra Parmesan cheese if desired.