01 - Lightly grease the inside of your slow cooker with butter or non-stick cooking spray.
02 - Melt butter in a saucepan over medium heat. Add garlic and onion; sauté for 2-3 minutes until softened and fragrant.
03 - Whisk cornstarch into the saucepan and cook for 1 minute. Gradually pour in half-and-half and chicken broth while whisking constantly. Bring to a gentle simmer and cook for 2-3 minutes until slightly thickened. Remove from heat.
04 - Stir in 1 1/2 cups shredded cheddar, salt, pepper, paprika, and thyme. Continue stirring until cheese is completely melted and sauce is smooth.
05 - Arrange half the sliced potatoes in the bottom of the slow cooker. Top with half the kielbasa rounds and half the cheese sauce. Repeat layers with remaining potatoes, kielbasa, and sauce.
06 - Cover and cook on LOW setting for 4-5 hours, or until potatoes are fork-tender.
07 - Sprinkle reserved 1/2 cup cheddar cheese over the top during the final 15 minutes of cooking time.
08 - Let the dish rest uncovered for 10 minutes before serving to allow the sauce to thicken slightly.