Preheat your oven to 425°F (220°C).
In a large braiser or Dutch oven, melt 2 tablespoons of butter over medium heat. Add the minced onion and cook for about 5 minutes, stirring occasionally until the onion becomes soft and translucent. Add the minced garlic, ham pieces, salt, and black pepper, cooking for an additional 30 seconds until fragrant.
Pour in the water, Better than Bouillon Baked Ham Base, and dissolve for a minute or two. Add heavy cream, stirring to combine.
Add the sliced russet potatoes to the skillet, making sure they’re evenly coated in the creamy sauce.
Increase the heat slightly and bring the mixture to a gentle simmer. Cover the skillet, reduce the heat to medium-low, and simmer for 15 to 20 minutes, stirring occasionally, until the potatoes are nearly tender when pierced with a knife.
Once the potatoes are nearly tender, Top with the mixed cheeses, spreading evenly over the potatoes. Transfer the braiser to the oven (with the lid off).
Bake the dish in the preheated oven and bake for 10 to 15 minutes, or until the cheese is melted, bubbling, and golden brown.
Allow the dish to cool for a few minutes before serving.