I haven't done a Cathedral windows yet, but have thought about it - a lot, and this version is new to me. For yours my easy way would be to make the background block a 9patch (no set-in pieces). Cut your green and pink fabrics the same size, stitch together RSF all round the edge. Cut a slit in the green, enough to turn inside out, press. Then pin in place on the block, fold the edges and stitch down.