1. Place potatoes in shallow baking dish. Microwave until skewer glides easily through flesh and potatoes yield to gentle pressure, 9 to 12 minutes, flipping potatoes every 3 minutes. Let potatoes cool for 10 minutes. Adjust oven rack to middle position and heat oven to 425° F.
2. Melt 3 tablespoons butter in 10-inch skillet over medium heat. Add shallots and cook, stirring occasionally, until softened, 2 to 5 minutes. Transfer shallots to bowl. Add bread pieces, 1/4 cup Parmesan, thyme, 1/4 teaspoon salt, and 1/4 teaspoon pepper to bowl with shallots. Toss to combine.
3. Halve each potato lengthwise. Using spoon, scoop flesh from each half into second bowl, leaving about 1/8- to 1/4-inch thickness of flesh. Place 6 shells cut side up on wire rack set in rimmed baking sheet (discard remaining 2 shells). Bake shells until dry and slightly crispy, about 10 minutes.
4. Meanwhile, mash potato flesh with ricer, food mill, or potato masher until smooth. Stir in egg, melted butter, 1/2 teaspoon salt, and remaining 1/4 cup Parmesan.
5. Remove shells from oven and reduce oven temperature to 375 degrees. Divide mashed potato mixture evenly among shells. Top each filled shell with bread mixture. Bake until bread mixture is spotty brown, about 20 minutes. Let cool for 5 minutes before serving.
TO MAKE AHEAD
Stuff potato shells as directed in step 5 but do not top. Store bread mixture at room temperature and refrigerate filled potatoes for up to 24 hours. To serve, top each shell and bake as directed, reducing oven temperature to 325° F and increasing baking time to 35 minutes.
Chef's Notes:
The skins of the sweet potato are edible and add an earthiness to the dish. When shopping, look for sweet potatoes that are uniform in size, with rounded ends.