Turned satin stitch
This is a variation of satin stitch: rather than the stitches remaining parallel across the design area, they are angled so that the stitch direction follows the shape of the design.
For more information see the entry for satin stitch.
Complete a split stitch outline around the shape and fill with split stitch padding. Bring the needle up on the inner curve of the shape just outside the split stitch outline where you can easily achieve the required angle for the first slanted satin stitch. Then take the needle down on the outer curve, just outside the split stitch.
Bring the needle up on the first side again, very close to the first stitch, just outside the split stitch. Take the needle down on the outside of the curve, angling the needle towards both the previous stitch and the split stitch.
Work towards the end of the shape. To change the angle gradually, bring the needle up a little closer to the previous stitch on the inner curve and take it down a little further away on the outer curve.
The last stitch should cover the split stitch outline. It can be finished by threading the needle under the satin stitch.
Using a new thread, resume stitching where you started. This time the direction of the stitch should be reversed, so bring your needle up on the outer curve of the shape.
To change the angle, bring the needle up a little further away from the previous stitch on the outer curve and tuck it closer to the previous stitch on the inner curve.
Structure of stitch
Various Authors, The Royal School of Needlework Book of Embroidery (2018) , p.330