Grease the insert of your slow cooker with non-stick cooking spray or butter to prevent sticking.
Wash and peel the potatoes. Slice the potatoes very thinly and uniformly. Consider using a mandolin slicer for best results.
In a medium saucepan, melt the butter over medium heat. Add in the onion and garlic and cook until translucent. Sprinkle the flour over the top and stir constantly to cook the mixture until lightly golden brown, about 2 minutes.
Gradually whisk in the chicken broth and heavy cream until smooth. Stir in the dried oregano, paprika, salt, and pepper. Continue cooking, stirring constantly, until the sauce thickens, about 3-4 minutes.
Layer one third of the sliced potatoes in the bottom of the greased slow cooker insert. Pour a third of the sauce over the potatoes followed by a third of the cheddar cheese and a third of the ham. Repeat the layers two more times.
Cover the slow cooker and cook on low heat for 4 to 5 hours, or until the potatoes are tender and the sauce is bubbly and creamy.
Once cooked, sprinkle with chopped fresh parsley for a pop of color and freshness, if desired.
Notes
I found that Yukon Gold potatoes work best with this recipe. Other varieties will work, but may not be as creamy or hold their shape as well. If the sauce separates, stir to recombine. If potatoes are ready early, keep warm in the slow cooker.