The easiest way to do it is probably to add the extra layer of batting after you have done the applique, but before layering. Place a piece of batting underneath your applique, then using water-soluble thread (at least in the top) machine stitch all around the applique about 1/4-inch from the applique's edge. Carefully cut away the excess batting close to the stitching line. Layer your quilt as usual, and quilt around the outside of the applique shape (to hold the extra batting in place permanently). When you wash the quilt, the water-soluble thread will disappear.
Superior Threads sells two grades of water-soluble thread. Alternatively, you can use regular thread when you baste the batting in place; just use longer stitches to make them easier to remove when the quilt is finished.
The most difficult part is cutting away the excess batting because you have to be very careful not to nip into your top fabric while you do it.
Also, it is recommended to use a high-loft poly for the extra layer of puffiness. Just be sure not to iron it.