This is a classic unilateral leg exercise with added overhead stability work for an efficient accessory exercise that improves strength, stability and mobility and symmetry both in the upper and lower body.
 
Place the top of one foot on a bench or split squat roller behind you, and the other foot on the floor in a lunge position. Hold a dumbbell, kettlebell or similar in the hand opposite of the forward leg, and hold overhead with a tightly locked arm and shoulder.
 
Squat as deep as possible without resting the knee on the floor, maintaining control of the overhead weight, and stand again. Place as much of the weight and effort on the front leg as possible without leaning forward unnecessarily.
 
Purpose
This exercise is a way to develop unilateral leg strength to maintain symmetry side to side, improve hip stability, strengthen and lengthen the hip flexors, and can also be used for encouraging lower body hypertrophy. The overhead component is a way to use training time more efficiently and use an exercise already being performed to also address overhead stability and to some degree mobility.
 
Programming
Perform this exercise after your primary lifting with other accessory work. Generally sets of 6-15 reps are appropriate depending on intent—initially, start with sets of 10, and then modify depending on whether you want to emphasize strength (fewer reps) or hypertrophy/stamina (more reps).
 
Variations
The length of the split can be changed to emphasize different parts of the leg—a closer foot will be more like an Olympic squat emphasizing the quads and glute, and a longer stance will be more like a lunge with more emphasis on glutes and hamstrings. The tempo can be adjusted as well—a slow eccentric motion (3-5 seconds) can help with hypertrophy in particular. An explosive concentric motion with a lift of the front foot off the ground can also be used.