I really like this exercise to help increase hip mobility while really blasting the legs.  The Bulgarian split squat by itself is tough enough but by performing this exercise from a deficit you can get additional benefits. Look closely at the range of motion the hip can go through to complete the movement when your squat leg is on a step. 

One way you can progress this exercise is to use dumbbells in each hand, which would requite additional muscle activation and stabilization.  However, a unique way to progress this exercise is to add a light dumbbell to the support leg side.  What this does is it encourages your hip external rotators and abductors to work harder eccentrically while the hip flexes to counterbalance the internal rotation and adduction that the hip want to go into due to that weight.  

When we think of core strength or stability I think there is a general misconception that everyone has a flexed posture. While it may be true very often, I have had a few athletes and patients who exhibit that excessive lumbar lordosis posture.  You can typically see it with their standing posture but it often becomes more evident when you get them exercising.  Anti-extension core exercises can be a way to correct this deficiency.   
Many low back injuries can occur as a result of uncontrolled extension, rotation, or flexion.  Therefore we must consider thinking about core training in these 3 realms.  When working with your athletes or patients, consider if they are too lordotic or too flexed.  Furthermore, consider if rotation is something that is inhibited or uncontrolled.  Core training is about motor control and increasing hip mobility and lumbar stability together so that a complicated movement can occur fluently.  
To perform this exercise take a stability ball or ab wheel.  Instruct the athlete or patient into neutral spine to begin.  Cue them to keep that neutral spine or "flat" back throughout the exercise.  When they begin to substitute the rollout ends.  We want to work on controlling that lumbar extension in this exercise.