Place potato halves into a large pot of salted water, bring to a boil, and reduce heat to medium-low. Cook until very tender, about 15 minutes. A knife should pierce the middle of a potato half easily. Transfer potatoes to a colander and drain thoroughly, about 5 minutes.

Preheat oven to 425 degrees F (220 degrees C).

Whisk mascarpone cheese in a mixing bowl until smooth. Stir egg yolk and milk into mascarpone cheese, whisking until smooth; season with salt, black pepper, and cayenne pepper.

Transfer potatoes to a separate large mixing bowl, add butter chunks to potatoes, and season with salt and black pepper. Mash butter into potatoes with a potato masher until fluffy; a few lumps are okay. Whisk mascarpone mixture into mashed potatoes.

Spread mashed potatoes into a 9x13-inch baking dish. Smooth the top and use the tip of a spatula to lightly press the potatoes and lift up to create little peaks and valleys in the top.

Bake in the preheated oven until potatoes are heated through and top is golden brown, about 20 minutes.