Ham and potatoes go together like Pooh and Piglet. They can manage quite well on their own, but when they’re teamed up, they rule the world.
Preheat the oven to 350 degrees. Lightly butter a 9-by-13-inch baking dish.
Melt 4 tablespoons of butter in a medium saucepan over medium-low heat. Whisk in the flour until there are no lumps. Cook, stirring, until it doesn’t smell like raw flour, a couple of minutes. Raise the heat to medium-high and slowly pour in the milk while whisking. Bring the milk to just a simmer and let thicken slightly (look for it to reach the consistency of heavy cream), 12 to 15 minutes, stirring throughout. Stir in the salt and pepper and turn off the heat.
Peel the potatoes. Adjust the mandoline to cut 1/8-inch slices. Carefully slice the potatoes into a large bowl.
Arrange two layers of potatoes in the prepared baking dish and sprinkle with a little salt. Top with of the Mortadella. Add one layer of potatoes and sprinkle with a little salt. Then another third of the Mortadella, another layer of potatoes and salt, and one last layer of mortadella. Arrange the remaining potatoes on top. Pour the white sauce over the potatoes; they will be mostly covered. Cover with foil and bake for 45 minutes. Remove the foil and continue baking until the sauce and potatoes begin to brown, about 45 more minutes. Without removing the pan from the oven, turn the broiler to high and broil to get more spots browned, about 3 minutes.
Remove from the oven and let rest for 10 minutes before serving.