Begin by preparing the ingredients. Thoroughly rinse the green beans and trim the ends. Peel the garlic clove and lightly crush it with the flat side of a knife so the flavors will release well during cooking. Keep the fresh rosemary handy and pat the lamb chops dry with paper towel.
Fill a pan with water and bring to a boil. Add the cleaned green beans and cook them until just tender in a few minutes. Drain the beans through a colander and let them steam dry briefly.
Meanwhile, heat the ghee in a frying pan over medium-high heat. Place the lamb chops in the pan and immediately add the crushed garlic and fresh rosemary to the hot fat. Fry the meat for about three to four minutes per side until golden brown, keeping the inside tender and light pink.
Remove the lamb chops from the pan and let them rest for a minute. Divide the warm green beans over the plates and place the meat alongside. Finally, drizzle a little of the remaining, spiced ghee from the pan over the lamb chops and serve immediately.