Cook sausage links in cooking oil in a medium skillet over medium heat for 10 minutes or until cooked through, turning frequently to brown evenly. Remove sausage from heat and allow to cool. Cut in 1/4-inch-thick slices and set aside.
Meanwhile, for dressing, whisk together olive oil, lemon peel, lemon juice, snipped basil, Italian seasoning, and garlic in a small bowl; set aside. Cut roasted red peppers into bite-size strips.
Layer sausage, red pepper strips, and olives in a 2-quart jar or two 1-quart jars. Pour dressing into jar(s), cover tightly, and refrigerate for 1 to 2 days. Turn jar(s) upside down occasionally to distribute the dressing.
Let stand at room temperature for 30 minutes before serving. Arrange on a platter; add cheese and garnish with basil sprigs, if desired. Makes 12 to 16 servings.