In a large Dutch oven, boil butternut squash in salted water until fork-tender. Drain and set aside to cool slightly.

Heat olive oil in a Dutch oven. Add half of the mushrooms and saut? on high heat until deeply brown in color and caramelized, about 5 to 7 minutes. Season generously with salt and pepper, remove to a plate, and repeat with remaining mushrooms. Set aside for later.

In a mini food processor, finely blitz shallots, garlic, and celery. Melt butter in the Dutch oven (without wiping it clean from the mushrooms). Add shallot-garlic-celery mixture, bay leaves, and dried thyme and saut? over low heat until shallots are translucent, about 2 to 3 minutes. Stir in arborio rice, coating each grain in the shallot-y butter and toasting the rice slightly, about 1 minute.

Splash in the wine and deglaze the bottom of the pot, scraping up any flavor bits. Once all the liquid has evaporated, lower the heat to medium and add a ladleful of stock (about 1/2 cup), stirring constantly until absorbed by the rice. Repeat with the rest of the stock, one or two ladlefuls at a time, until the rice is cooked to your liking. This process takes about 18 to 20 minutes. Remove from heat, cover, and set aside to finish cooking, about 5 minutes.

Pur?e the cooled butternut squash with a hand blender along with heavy cream and the egg yolk. Fold squash mixture into risotto; it should melt into the rice and loosen it a bit. Stir in the cheese and half of the cooked mushrooms. Taste for seasoning; add more salt and pepper if needed.

Spoon the risotto onto each plate and top with the remaining cooked mushrooms. Finish with a dusting of Pecorino.