Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.
Heat the oil in a small skillet over medium-high heat. Add the mushrooms, shallot , salt, and pepper. Cook and stir until the mushrooms break down into a paste, 5 to 10 minutes. Remove from the heat and allow to cool slightly.
Lay the sheet of puff pastry out on a clean work surface and roll out to fit the length of your rabbit loin. Spread the mushroom paste over the surface. Place the rabbit loin on the center and arrange the asparagus alongside the rabbit. Roll the pastry around the rabbit and asparagus into a tight closed cylinder, pinching the ends to seal. Place on prepared baking sheet, and brush the top of the pastry with egg yolk.
Bake in preheated oven until the pastry is a deep golden brown, for 10 to 13 minutes. Remove from the oven and let rest for 5 minutes. The meat should reach an internal temperature of at least 145 degrees F (65 degrees C).
While the rabbit is cooking, heat the demiglace in a small skillet over medium heat. When melted and hot, stir in the butter until melted and remove from the heat.
To serve, cut the pastry in half crosswise, and set in the center of a serving plate. Drizzle the sauce around the plate.