For the potato and celery root puree:
Place the potatoes and diced celery root in a saucepot with enough cold water to cover. Add salt and bring to a boil. Allow to cook until cooked through and fork tender, about 15 minutes. Drain the potatoes, reserving 1/2 cup potato water for the sauce, and add the potatoes to a potato ricer over a bowl. Add the butter, making sure it is equal parts butter and mashed vegetables, and stir to combine. Taste the mixture and season with salt.
For the salad:
Place the shallot, salt, apple cider vinegar into a bowl and drizzle in about 1/2 cup extra-virgin olive oil. Taste and re-season, if needed, and pour over the julienned celery root. Add the apples and toss to coat. Just before serving add the celery leaves to the salad and toss to combine.
For the scallops:
Season the scallops on both sides with salt. Place a large saute pan over medium heat and add the oil. Once heated, add the scallops and sear until golden brown on both sides, about 2 to 3 minutes per side. Be careful not to overcook. Ideally you are looking for a tender middle, medium at the most.
Turn down the heat to medium-low on the pan and add the butter, thyme sprigs and the juice of 1 lemon. Once the butter has melted and browned, add about 1/2 cup potato water, season with salt and taste. Turn off the heat and set aside.
For each serving:
For each serving, plate a spoonful of the mashed potatoes in the middle of the plate. Top with 3 scallops and a large spoonful of the salad over the top. Spoon the sauce over the scallops and around the plate.