Boil 2 pounds potatoes in their skins until they are soft, then let them cool completely. I recommend cooking the potatoes the day before and letting them cool overnight. Once fully cooled, peel them and slice into thin pieces.
Remove the shells from 2 hard-boiled eggs, and finely chop them with a knife.
Peel and finely chop 1 medium onion. Heat 2 Tablespoons canola in a pan over medium-high heat. Fry the onions in the hot oil until golden brown, stirring frequently. Then add 9 ounces smoked ham (diced), reduce the heat slightly, and fry for a further two minutes.
Grease a baking dish with ½ Tablespoon solid fat and sprinkle with 2 Tablespoons breadcrumbs. This step makes it easier to get the finished potato gratin out of the dish without it sticking to the sides.
Start stacking the potato layers in the prepared baking dish. Layer the sliced potatoes first, season them with salt and ground pepper. Continue with the fried ham and onion, and finally the chopped egg. Go on with another layer of potatoes (salt and pepper again), then a layer of ham and egg, and finish with sliced potatoes, that you salt and pepper.
Heat the oven to
350 °F. Place the dish of layered potatoes in the oven and bake for 10 minutes. Meanwhile, in a bowl, whisk 1 cup half and half with 2 fresh eggs. After 10 minutes, remove the potato dish and pour the milk and egg mixture evenly over the potatoes. Spread 3 ½ ounces grated cheese evenly over the surface.
Return the potato dish to the oven and bake until golden on top. This takes about 30 minutes.