Preheat the oven to 350 degrees . Place the ham in a roasting pan with 1 cup water and bake until heated through, about 1 hour. Let the ham cool slightly, about 10 minutes.
Meanwhile, in a small saucepan, melt the jelly over low heat. Remove from heat and stir in the tomatillos. Brush the ham (except for the cut side) with the jelly-tomatillo glaze, then gently pat the cilantro onto the glaze.
Scoop the avocado flesh into a bowl. Add lime juice and salt and mash with a fork.
Melt 2 tablespoons butter in a large skillet over medium heat. When the butter stops foaming, crack 4 eggs into the pan, cover and cook until the yolks are slightly firm. Transfer the eggs to a serving platter and repeat with the remaining 2 tablespoons butter and 4 eggs.
Scoop the guacamole onto each egg yolk. Slice the ham and serve with the eggs; serve the leftover guacamole on the side.