Place the garlic, oregano, thyme, 1 tablespoon olive oil, and the lemon zest (reserve the juice for later) in a mini or regular-sized food processor, and season with salt and pepper. Process until it becomes a paste (if you are a mortar and pestle type of cook, you can use that instead).
Rub about ⅔ of the herb paste on the top of the lamb, the side that was cut for butterflying. Then roll up the lamb and tie it well with kitchen twine at 1 ½ inch intervals to keep it tightly rolled. Rub the rest of the paste over the outside of the lamb, place in a pan or container, and refrigerate from 1 hour to 24 hours uncovered.
Take the lamb out of the fridge and let it come to room temperature while you preheat the oven to 450 F. Place the lamb in a roasting pan and roast for 20 minutes, then reduce the heat to 375 F and roast for another 50 to 70 minutes. An internal thermometer inserted into the thickest part of the roast should read 125 F for medium-rare.
While the lamb is cooking or resting, make the Creamy Feta Sauce: In a small bowl, combine the Greek yogurt, 2 tablespoons olive oil, 1 tablespoon fresh lemon juice, dill, and minced garlic. Add the feta and stir, lightly mashing it into the mixture, using a fork. Taste and season as needed with salt and pepper. Spring over some small dill sprigs, if using.
When the lamb is cooked, let it rest on a cutting board for 20 minutes. Slice the lamb against the grain, remove the string, and transfer to a serving platter. Sprinkle the reserved 1 tablespoon lemon juice over the sliced lamb and give the slices a light seasoning of salt and pepper. Serve warm with the feta sauce on the side.
Notes
When a cut of meat is butterflied it means it is cut almost in half horizontally, and opened flat so that it cooks more quickly and more evenly. In the case of larger, thicker pieces of meat, it might be sliced in more than one place so that it unfolds into a flatter cut of meat. Ask your butcher to butterfly the lamb for you.
Leftover lamb can be used in all kinds of ways. Sandwiches, obviously: pile thin slices on a halved baguette or some good thick peasant bread and slather on some of the feta sauce, or try Herbed Mayonnaise, Spicy Salsa Verde, Green Olive and Ramp Tapenade, Sriracha Mayo, or maybe just some leftover jarred pesto or another condiment you have in your fridge or pantry.
Slices can be added to a Greek Salad for a fantastic dinner or lunch later in the week. And I always make too much lamb in the hopes of a shepherd’s pie being on the horizon (which happily was the case here!)