01 - Lightly grease the inside of your slow cooker with butter or non-stick spray.
02 - In a saucepan over medium heat, melt the butter. Add garlic and onion; sauté 2-3 minutes until soft.
03 - Whisk in cornstarch; cook for 1 minute, then slowly add half-and-half and chicken broth, whisking until smooth. Bring to a gentle simmer and cook until slightly thickened, 2-3 minutes. Remove from heat.
04 - Stir in 1 1/2 cups shredded cheddar, salt, pepper, paprika, and thyme, stirring until cheese melts.
05 - Layer half of the sliced potatoes in the bottom of the slow cooker. Top with half the kielbasa and half the sauce. Repeat layers with remaining potatoes, kielbasa, and sauce.
06 - Cover and cook on LOW for 4-5 hours, or until potatoes are fork-tender.
07 - Sprinkle reserved 1/2 cup cheddar over the top during the last 15 minutes of cooking.
08 - Let sit 10 minutes before serving for the sauce to thicken.