Cut a small slice off the bottom of each squash half so it rests flat. Brush the insides with 1 teaspoon oil; sprinkle with 1/4 teaspoon each salt and pepper. Place in a 9-by-13-inch (or similar-size) microwave-safe dish. Cover with plastic wrap and microwave on High until the squash is fork-tender, about 12 minutes.
Meanwhile, heat 1 tablespoon oil in a large skillet over medium heat. Add onion; cook, stirring, until starting to brown, 2 to 3 minutes. Add garlic; cook, stirring, for 1 minute. Stir in water, tomato paste and the remaining 1/4 teaspoon each salt and pepper. Stir in chard, cover and cook until tender, 3 to 5 minutes. Stir in white beans and olives; cook until heated through, 1 to 2 minutes more. Remove from the heat.
Position rack in center of oven; preheat broiler.
Combine breadcrumbs, Parmesan and the remaining 1 tablespoon oil in a bowl. Fill each squash half with about 1 cup of the chard mixture. Place in a baking pan or on a baking sheet. Sprinkle with the breadcrumb mixture. Broil in the center of the oven until the breadcrumbs are browned, 1 to 2 minutes