Bring a large pot of salted water to a boil for the pasta. Trim the tough stems at the bottoms of the chard leaves and discard. Separate the tender stems from the leaves, and wash both well. Cut the stems into ¼-inch pieces. Coarsely shred the leaves.

Heat a large skillet over medium-high heat. Add the olive oil. When the oil is hot, add the onion and garlic, and cook until the onion is golden, about 5 minutes. Add the chard stems, and cook until they are almost tender, about 5 minutes. Add 2 cups pasta water, and boil rapidly until reduced by about a third, about 3 minutes. Add the chard leaves, and season with the salt and crushed red pepper. Cover, and simmer until the stems and leaves are both very tender, about 10 minutes.

While the chard cooks, add the pasta to the boiling water. When the sauce is ready and the pasta is al dente, remove the pasta with tongs and transfer directly to the simmering sauce. Add the fresh ricotta and the walnuts, and toss to melt the ricotta into the sauce, just a minute or two. Add a little pasta water if the sauce seems dry. Remove the skillet from the heat, sprinkle with the grated cheese, toss and serve.