Polenta and Sausage Hash

Pierce sausage links with a fork and place in a saucepan. Cover with water and bring to a simmer. Simmer over low heat for 10 minutes. Transfer to a cutting board and let cool slightly; cut into thin rounds. Meanwhile, pat polenta dry and cut into 1/2-inch-thick slices. Stack slices, 4 or 5 at a time, and cut into quarters. Pat slices dry and set aside. Cook the sausage slices in a large nonstick or cast-iron skillet, stirring over medium-high heat, until browned, 3 to 5 minutes. Transfer to a plate lined with paper towels. Add 1 teaspoon oil to the pan. Add onions and cook, stirring, until soft, 2 to 3 minutes. Add peppers, season with salt and pepper and cook, stirring, until tender, about 3 minutes longer. Transfer the vegetables to a plate. Wipe out the pan and add the remaining 2 teaspoons oil to the pan; tilt to coat the bottom evenly. Add the reserved polenta and cook, stirring occasionally, until nicely browned, 3 to 5 minutes. Add the reserved vegetables and sausages to the skillet and shake the pan over the heat until everything is heated through. Taste and adjust seasonings with salt and pepper. Remove from the heat, sprinkle with cheese and garnish with parsley. Serve immediately.