Do you want texture in the embroidery? If so, quilting through thin batting and cheese cloth layered in a hoop will work if you are hand embroidering it. I would hand stabilize it before hand, and them have fun. If you want the embroidery to be the prime focus and only textured by stitching, then I would just do it through the pieced square since it is reinforced by the interfacing. For machine embroidery, follow someone else’s advice, since I have no clue.