Peel the yukon gold potatoes and slice them into 1/8-inch thick rounds—a mandoline slicer works beautifully here and keeps all slices uniform for even cooking. Mince the garlic cloves fresh (I always do this just before cooking since pre-minced garlic loses its punch), dice the onion into small pieces, and dice the ham into 1/2-inch cubes. Shred the cheddar cheese from a block rather than using pre-shredded, as it melts far more smoothly without the anti-caking agents. Have all ingredients measured and ready before you begin cooking.
Melt the butter in a medium saucepan over medium heat, then add the diced onion and cook for 2-3 minutes until softened and fragrant. Add the minced garlic and cook for another 30 seconds until aromatic. Sprinkle the flour over the mixture and stir constantly for 2 minutes to create a roux—this cooks out the raw flour taste and helps thicken the final sauce. Gradually whisk in the chicken broth and cream, stirring continuously to avoid lumps, then add the oregano, paprika, salt, and pepper. Simmer for 3-4 minutes until the sauce thickens slightly and coats the back of a spoon.
Grease the slow cooker lightly. Begin layering by placing about 1/3 of the sliced potatoes on the bottom, then pour about 1/3 of the creamy sauce from Step 2 over them. Sprinkle with 1/3 of the diced ham and about 3/4 cup of the shredded cheese. Repeat this layering two more times, ending with a final layer of potatoes, then sauce, ham, and cheese on top. The key is distributing ingredients evenly so every bite has potatoes, ham, sauce, and cheese. Cover and cook on low for 4-5 hours until the potatoes are fork-tender but not falling apart—I like to check them at the 4-hour mark since crockpots vary in temperature.
Once the potatoes are tender and the cheese is melted and bubbly, turn off the slow cooker and let the dish rest for 5 minutes—this helps it set slightly and makes serving cleaner. Garnish generously with fresh parsley and serve directly from the slow cooker or transfer to a serving dish.