Heat oven to 325º. Butter or spray 9 x 13 casserole dish with Pam.
In a large Dutch oven on medium/high heat, sauté sliced sausage in a bit of olive oil until browned. Remove to a bowl.
Reduce heat to medium and add butter. Sauté onions, carrots, potatoes, bell pepper, and cabbge until lightly caramelized – about 20 minutes. Add salt, pepper and onion soup mix. Stir in milk, vinegar, and sugar. Add sausage and drippings. Bring to boil. Reduce heat to medium-low; simmer for 5 minutes. Remove pot from heat and let cool slightly, then gently stir in eggs.
In a large zip-lock bag, crush crackers with caraway seeds. Into the pot of veggies and sausage, add ½ of the cracker mixture. Pour into prepared casserole dish. Dust top evenly with remaining crackers. Bake at 325º for 45 minutes, or until heated through and top is golden brown.