If you have a slow cooker that cooks a little on the hot side, lightly spray the sides of the slow cooker about halfway up.
Cut sausage into 1/4" half moons. Place in slow cooker and spread evenly around the edges leaving a well in the center.
Dice potatoes and place in the well on the bottom of the slow cooker. Sprinkle with half the spices.
Drain green beans and place on top of the potatoes. Sprinkle remaining spices over the top. Do not stir.
Cook on HIGH for 3-4 hours or LOW for 6-7. DO NOT STIR.
Check halfway to 2/3 of the way through cooking. If the sausage is getting too toasty, carefully run a spatula around the edges and mix the sausage up a bit, but don't stir the whole thing together. We're trying to leave the green beans on top so they don't overcook, and the sausage along the sides to get browned. Once cooking is complete, stir it all together.
Optional:Serve with garlic bread or other crusty bread on the side.