Preheat oven to 400 degrees. Butter a 9-inch square baking dish. Process almonds and brown sugar in a food processor until almonds are finely chopped. Add butter; process until just combined.
Place apricot halves, cut sides up, in buttered baking dish. Cover top of each apricot half with almond mixture. Bake until apricots are soft and almond mixture is deep golden brown, 15 to 20 minutes. Transfer 3 apricot halves to each serving plate. Serve warm.