Trim lamb of fat and silver connective tissue. Butterfly lamb and cut into 2-3 pieces that can roll into individual roasts.
Adjust oven rack to lower-middle position and preheat oven to 275°F. Heat olive oil in a small saucepan over medium heat until shimmering. Add garlic, shallot, anchovies, rosemary, lemon zest, and red pepper flakes. Cook, stirring occasionally, until shallots and garlic are softened, about 5 minutes. Transfer to a small bowl. Add salt and pepper and mix with a fork to combine.
Rub half mixture into insides of lamb roasts. Roll and tie securely at 1-inch intervals with butcher’s twine. Rub remaining mixture over exterior of lamb roasts. Cook immediately or let rest uncovered in the refrigerator for up to one night for best flavor and texture.
When ready to cook, place lamb on a wire rack set in a foil-lined rimmed baking sheet. Transfer to oven and roast until an instant read thermometer inserted into coolest section of lamb registers 125°F to 130°F (52°C – 54°C)for medium-rare, checking after 10 minutes, then every 5-10 minutes. Remove from oven and let rest for 20 minutes.
While lamb is resting, add butter and rosemary to a skillet. Baste lamb with butter to sear outside. Remove and let rest 5 minutes. Remove twine with kitchen shears, transfer lamb to cutting board, slice into 1/4 inch slices, and serve.