Preheat the oven to 500 degrees F with a baking stone on the bottom rack. Invert a baking sheet and top with a sheet of parchment paper.
Melt the butter in a small saucepan over medium heat. Stir in the flour to make a smooth paste and cook 1 to 2 minutes to remove the raw flour taste. Whisk in the beer and bring to a simmer to thicken. Whisk in the cream. Simmer the sauce until smooth and thick, about 4 minutes. Whisk in the cayenne and nutmeg and season with salt. Transfer to a bowl and let cool, about 10 minutes.
Lightly oil your hands and the countertop with oil. Press and stretch the dough ball into a thin round, 10 to 11 inches in diameter. Transfer to the parchment-lined-baking sheet and press back into shape if it has shifted. Spread the cream sauce on the crust (you will have some left over) almost to the edges. Sprinkle with the mozzarella, Jarlsberg and Parmesan. Scatter the prosciutto over top.
Slide the pizza, still on the parchment, onto the baking stone. Bake until the cheese is browned and bubbly and the crust is browned and crisp on the bottom, 7 to 8 minutes.
Top the pizza with the arugula, a pinch of salt and drizzle with oil. Cut into slices and serve.