Separate garlic cloves, but leave peels on. Put cloves together with olive oil and rosemary sprig in small heavy saucepan with lid; place pan uncovered over medium heat until garlic just starts to sizzle. Turn heat down to low and cover with lid. Cook gently until garlic is easily pierced with a paring knife – about 20 minutes. Do not let garlic burn! Remove rosemary sprig and discard. Remove garlic cloves from oil, let them cool, and then peel; the peels should virtually fall off. Reserve garlic and oil separately.
While garlic is cooking, peel butternut squash and cut into 3/4-inch cubes. Place squash in roasting pan, lightly coat it with olive oil, salt and pepper, and place in preheated oven. Roast until the squash can be pierced easily with a fork and is lightly browned – about 30 minutes. Remove and set aside.
Pat lamb chops dry with paper towels and salt and pepper generously. Place large skillet over medium high heat (you don’t want to crowd the chops); add 1 tbsp olive oil and lamb chops. Sear on one side for 4 minutes and turn. Sear other side for about 2 minutes for rare or 4 minutes for medium. Remove lamb to heated plate, tent with foil, and let rest for 5 minutes
Arrange roasted squash on dinner plates. Place lamb chops on top and garnish with the roasted garlic cloves. Drizzle reserved garlic oil over the lamb.