Preheat oven to 350 degrees F (175 degrees C). Grease a 9 inch square pan.
Combine 2 cups flour, butter, 1/2 cup confectioners' sugar, and 1/2 teaspoon chipotle chile powder in a food processor; pulse until mixture resembles coarse crumbs. Press the mixture into the prepared pan.
Bake in preheated oven for 30 minutes, or until firm and golden. Remove from oven and allow to cool at least 20 minutes in the pan.
Reduce the oven temperature to 325 degrees F (165 degrees C).
In a small bowl, whisk together the preserves and 1/2 teaspoon chipotle chile powder; spread over the cooled crust. Whip eggs with a wire whisk until foamy. Beat in sugar, lemon juice, and salt until the sugar has dissolved. Sift together 1/3 cup flour and baking powder; whisk into eggs until smooth. Pour onto the preserve-topped crust.
Bake in preheated oven an additional 35 to 40 minutes, until the center of the egg mixture has set. Sift together 1/3 cup confectioners' sugar with 1/2 teaspoon chipotle powder, and sprinkle over hot lemon bars. Cool completely before cutting into bars.
