Add the 3 potatoes to a medium size saucepan, fill the pan 3/4 full of water. Bring the water to a rolling boil and reduce to medium heat. Cook the potatoes 10 minutes. Remove from heat and allow to cool.
Preheat oven to 400 degrees F. Spray an 11 x 7-inch baking dish with cooking spray and set aside.
In a deep skillet or sauce pan combine the butter over medium heat, add the shallot and garlic and sauté until fragarant. Stir in the milk, heavy cream, shredded cheddar, salt and pepper. Bring the mixture to a simmer, stirring occasionally. When the mixture has thickened remove from the heat and set aside.
In the casserole dish layer the chopped parboiled potatoes, broccoli and ham. Top with the cheese sauce.
Top with shredded cheddar cheese and bake 20-25 minutes until the potatoes are cooked through (check with a fork)
Allow the dish to rest at least 10 minutes before serving.
Serving: 3/4 heaping cup, Calories: 390kcal, Carbohydrates: 21g, Protein: 24.7g, Fat: 23g, Cholesterol: 92mg, Sodium: 360mg, Fiber: 2.8g, Sugar: 5.6g