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

While the pasta cooks, wash the Swiss chard thoroughly. Separate the leaves from the stems. Chop the stems into 1/2-inch pieces and coarsely chop the leaves into 1-inch strips.

In a large skillet over medium heat, add the olive oil. Once shimmering, add the minced garlic and red pepper flakes (if using). Sauté for 1 minute until fragrant, being careful not to burn the garlic.

Add the chopped Swiss chard stems to the skillet and sauté for 3-4 minutes until slightly softened. Then, add the chopped Swiss chard leaves to the skillet, stirring occasionally, until wilted and tender, about 4-6 minutes.

Pour in the vegetable broth (or reserved pasta water) and bring to a gentle simmer, scraping up any browned bits from the bottom of the pan. Stir in the lemon juice and lemon zest.

Add the drained pasta to the skillet with the Swiss chard mixture. Toss well to coat. Stir in the 1/2 cup of grated Parmesan cheese. Season with salt and freshly ground black pepper to taste. If the pasta seems dry, add a splash more reserved pasta water.

Divide the pasta among serving bowls. Garnish with additional fresh Parmesan cheese and a sprinkle of red pepper flakes if desired. Serve immediately.