Pour butter into a greased 8-in. square baking dish; sprinkle with brown sugar and cinnamon. Arrange apricot halves, cut side down, in a single layer over top; set aside.
In a small bowl, beat shortening and sugar for 2 minutes or until crumbly. Beat in egg. Combine the flour, baking powder and salt; gradually add to crumb mixture alternately with milk just until combined. Spread over apricots.
Bake at 375° for 30-40 minutes or until a toothpick inserted in the center comes out clean. Cool for 10 minutes before inverting onto a serving plate. Place a pecan half in the center of each apricot half. Serve warm.