sounds like a quilt as you go- or Cotton Theory quilt- there are tutorials here, on u-tube, all over showing how to add the sashing between blocks- just look up either 'Cotton Theory Quilting' or quilt as you go.
basically- you stitch the sashing strips to one side of a block- fold it out to cover the seam between blocks and stitch down on the second block- some people whip stitch this by hand- many machine stitch them- some use decorative stitches.