When oil is shimmering add the shallots and a generous pinch of salt. Reduce the heat to its lowest setting and cover. Let cook for 15 minutes
When the potatoes are tender, drain them and place them on the baking sheet cut-side-down. Drizzle the potatoes with olive oil and salt. Transfer the potatoes to the oven and roast for 25 minutes.
The shallots should be a deep amber color by now. In a bowl, stir to combine the shallot mixture, yogurt, scallions, honey, and salt.
Spoon the yogurt mixture onto a large plate and spread it with the back of your spoon to form a bed for the potatoes. Place potatoes on top of the yogurt. Top with a handful of the mixed greens.