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.