In a large skillet, add enough water to reach a depth of 1/2 inch and bring to a simmer over medium heat. Add the spinach and cook, stirring, until wilted, about 2 minutes. Drain in a colander; wipe the skillet clean. Add the olive oil to the skillet and heat over medium heat. Add 1 tablespoon roasted garlic and cook for 30 seconds. Add the wilted spinach and 2 teaspoons salt and toss. Remove from the heat and cover to keep warm.
Preheat a grill pan over high heat. In a small saucepan, cook the vinegar, shallots and 1 teaspoon each salt and pepper over medium heat until almost dry, about 5 minutes. Season the lamb chops with salt and pepper and grill for 4 minutes on each side for medium.
Using a blender, combine the reserved vinegar mixture, egg yolks and remaining roasted garlic on low speed. With the machine on, slowly add the hot butter until the sauce is thickened; season with salt. Transfer to a serving bowl and stir in the mint.
Place the spinach on a platter, top with the lamb chops and serve with the sauce.