Step 1Heat 1 tablespoon oil in large skillet over medium heat, swirling oil to coat pan. Add sausage and saute until meat is no longer pink, about 5 minutes. Transfer to plate using slotted spoon; set aside.
Step 2Drain fat from skillet. Add 2 tablespoons oil, and saute onion, celery and carrot over medium heat until tender, about 5 minutes. Add tomatoes with juice. Stir to combine, then simmer, uncovered, until sauce is thickened, about 15 minutes.
Step 3Meanwhile, heat 12-inch skillet or stove-top grill pan over medium-high heat. Add 2 tablespoons oil and fry polenta squares until lightly browned on both sides, 4 to 5 minutes. Do not crowd pan; fry in 2 batches, if necessary. Place on baking sheet and keep warm in 275-degree oven until sauce is done.
Step 4Add sausage and parsley to sauce. Stir to combine and cook until heated through, about 5 minutes. Taste sauce and add salt and pepper, if desired. Place 2 squares polenta, slightly overlapping, on each plate. Spoon generous amount of sauce over and serve immediately.