Another case of serious curve-piecing avoidance here.
Print or trace the block diagram onto freezer paper and cut into four squares on the lines. (I had already made the one square before I realized I hadn't taken a photo.)
Out of background fabric, cut four 3" squares.
Out of main fabric, cut four 3" squares.
Iron a freezer paper section onto the center of a main fabric square, avoiding the center curved section.
Place a background square on the table and place the square with the freezer paper ironed onto it on top.
Baste the three layers together VERY securely, especially the little corner triangle. You will be reverse applique-ing the center curved section, so don't baste too close to that edge.
Inserting the point of your scissors between the freezer paper and top fabric layer, cut out the freezer paper on the lines as follows. Because you didn't iron the freezer paper to the fabric here, this should be easy.
Press the section again, to make sure the freezer paper is attached properly.
Insert the point of your scissors between the main and background fabric layers and cut out the center curved section, leaving a small seam allowance. Clip the curved edge every ¼" or so almost to the seam line.
Reverse applique the two edges. Trim the seam allowances to 1/4". The squares should be 2 3/4" x 2 3/4". Carefully remove the freezer paper and press the block section.
Repeat for all four sets of squares. You may want to cut away some of the background fabric in the back of the sections at this point to reduce bulk.
Sew pairs of square sections together, being careful to align the corners of the center square. Press the seams open.
Sew the two resulting sections together. Press the seams open.
My little center square isn't perfect, but I don't think it would have looked better had I tried to piece it.