Preheat your oven to 425F. Score the fat cap of the lamb chops in a crosshatch pattern and season it generously with salt and pepper.
In a small bowl, combine the olive oil, garlic, sage, and thyme. Rub the mixture over the lamb and set it aside to marinate while you make the sides.
Bring a large pot of salted water to a boil. Add the potatoes and cook for 12-14 minutes, or until the potatoes are fork tender.
Remove the potatoes from the water and pat them dry on a towel (be careful, they’re hot). Gently smash the potatoes with a potato masher (or the flat side of a cup). Place the smashed potatoes on the sheet pan (try to make sure they don’t take up more than ¼ of the sheet pan) and drizzle them with olive oil and sprinkle with salt.
Bake for 10 minutes while you prepare the other sides.
Combine the carrots, olive oil, and salt in a small bowl and set aside until ready to use.
Combine the green beans, olive oil, and salt in a small bowl and set aside until ready to use.
Add the carrots and green beans to the sheet pan, making sure it’s not overcrowded– if it is, you may need to use two sheet pans.
Wrap the exposed bones of the lamb with aluminum foil and place it fat side up on the sheet pan. Bake for 15 minutes, then turn the heat down to 350F and bake for an additional 10 minutes, or until your desired doneness.
Remove the sheet pan from the oven and cover it with foil. Allow the lamb to rest for 10 minutes before slicing.