Set a large pot of salted water to boil for pasta. Meanwhile, in a large nonstick skillet, heat 1 tablespoon oil over medium. Add sausage and cook, stirring occasionally and breaking sausage into pieces, until cooked through and lightly browned, 10 to 12 minutes.
Add remaining oil, chard stems, artichoke hearts, and garlic; season with salt and pepper. Cook until chard stems soften slightly, 3 to 5 minutes. Add chard leaves and cook, stirring, until wilted, 3 to 5 minutes. Remove from heat.
Add pasta to boiling water; cook until 2 minutes short of al dente. Add sun-dried tomatoes and cook 2 minutes. Reserve 1 cup pasta water and drain pasta; return to pot.
Pour half of reserved pasta water into a small bowl. Add tomato paste and whisk to combine. Add tomato paste mixture, sausage mixture, Parmesan, basil, and red pepper flakes to pasta in pot. Toss to combine, adding reserved pasta water if necessary. Season with salt and pepper.