In a food processor, combine the flour, baking powder, salt and shortening; cover and process until mixture resembles coarse crumbs. While processing, gradually add water until dough forms a ball.
Transfer to a floured surface. Roll dough into a 10x8-in. rectangle. Cut into sixteen 10x1/2-in. strips. Twist each strip 4 times and place on baking sheets. Brush with oil. Combine coarse salt and thyme; sprinkle over breadsticks.
Bake at 350° until golden brown and crisp, 18-20 minutes. Cool on a wire rack.