Preheat oven to 375 degrees F.
Keeping the whole onions intact, peel away the outer layer. Carefully trim root ends with a paring knife, so they are flat. Cook the onions in a large pot of boiling water until tender, about 10 minutes. Drain and let cool.
Meanwhle, combine bread with milk in a small bowl; let soak for 10 minutes. Squeeze bread almost dry and, with your fingers break it into a large bowl. Stir in egg, mushrooms, capers, parsley, garlic, salt and pepper. Set aside.
Cut onions in half horizontally. Scoop out some of the center of each onion and chop coarsely. (Reserve the onion halves). Add the chopped onion to the bread mixture and mix well. Fill the onion halves with the bread mixture and sprinkle with dry breadcrumbs.
Arrange the onions in a shallow 2-quart baking dish and drizzle with oil. Bake, uncovered, until the tops are golden and the onions are heated through, about 25 minutes.
Make Ahead Tip: Prepare through Step 3; cover and refrigerate for up to 8 hours.
1 starch, 1 vegetable, 1/2 fat