Preheat the oven to 400˚ F. Add the sweet potato chunks to a baking dish. Drizzle lightly with olive oil and season with salt and pepper. Bake until just fork tender, about 12-15 minutes. Remove from the oven but maintain oven temperature.
Line a rimmed baking sheet with foil. Remove the stems from the mushrooms and carefully scrape the gills from the caps with a spoon or paring knife; discard. Place the mushrooms caps on the baking sheet. Drizzle each lightly with olive oil. Roast the caps about 10 minutes. Remove from the oven, maintaining the oven temperature.
While the mushrooms are baking, add about 2 teaspoons of olive oil to a medium skillet over medium-high heat. Add the onion and celery to the pan and sauté just until beginning to soften, about 5 minutes. Stir in the thyme and sage and cook 1 minute more, until fragrant. Remove the pan from the heat and set aside to cool for a few minutes.
Gently stir in the bread cubes, vegetable stock, sweet potatoes, and egg. Season with salt and pepper. Mound a portion of the stuffing mixture into each mushroom cap. Return the pan to the oven and bake 15 minutes more, until the stuffing is golden brown. Serve immediately.