Prepare pasta according to package directions. Drain; rinse briefly in colander with cool water. Set aside.
While pasta is cooking, melt 2 tablespoons butter in sauté pan. Add okra; sauté over medium high heat until okra is softened and starts to brown. Transfer to plate; set aside.
In same sauté pan, melt remaining butter. Sprinkle flour over butter; whisk to form roux. Continue whisking constantly approximately 30 seconds. Slowly add chicken broth and milk, whisking constantly. Add minced garlic. Slowly mix in shredded fontina until smooth. Fold in pasta and stir to combine.
Stir in Swiss chard leaves, zucchini, and sautéed okra, mixing well. Serve immediately.