Preheat oven to 450°F. Trim root end of each onion about 1/4-inch, keeping the root end intact. (This will help the onion sit flat in the pan and keep the filling inside.) Peel the onions. Cut off one-fourth of each onion top (on opposite end from root), leaving about a 3-inch-tall onion (discard onion tops or reserve for another use).

Using a melon baller or small spoon, carefully scrape and remove the inside of each onion, leaving the outer 1 to 2 layers intact and keeping the base slightly thicker; reserve 1 cup of the scooped onion scraps. (Discard the remaining onion scraps or reserve for another use.)

Place the hollowed-out onions, open-sides up, in a 9-inch-square metal baking pan. Pour 1 cup water around the onions; cover the pan with foil. Bake until softened, about 20 minutes. Remove the foil; bake until the onions start to brown around the edges, 10 to 12 minutes more. Remove from the oven; carefully discard the hot water from the pan. Reduce oven temperature to 375°F.

Meanwhile, combine mushrooms, the reserved 1 cup onion scraps and the remaining 2 tablespoons water in a large nonstick skillet. Bring to a simmer over medium-high heat; cook, stirring occasionally, until the vegetables are tender and the pan is dry, about 7 minutes. Add bread cubes and garlic; cook, stirring often, until warmed through and fragrant, about 2 minutes. Transfer to a medium bowl; let cool for 2 minutes. Add 1/4 cup Gouda, cream cheese, thyme, pepper and salt; stir until thoroughly combined. Stuff each onion with mushroom mixture (about 1/2 cup per onion); top evenly with the remaining 1/4 cup Gouda.

Bake until the cheese is melted and golden brown in spots, about 15 minutes. Transfer to a platter; garnish with additional thyme, if desired.