Preheat oven to 450°.
Peel onions, leaving root ends intact. Trim top third of each onion; reserve for another use. Arrange onions, cut sides down, in an 8-inch square baking pan coated with cooking spray; add chicken broth. Cover pan with foil; bake at 450° for 30 minutes. Uncover and bake an additional 30 minutes. Carefully turn onions over with a spatula; bake an additional 30 minutes or until onions are soft and liquid has almost evaporated. Remove from oven.
Combine feta, breadcrumbs, thyme, and pepper; stir with a fork until well blended. Gently pat cheese mixture evenly onto cut sides of onions. Broil onions until cheese mixture begins to brown (about 1 minute).