Combine the lamb, curry paste, olive oil, and salt in a bowl. Use your hands to massage the curry and oil into the lamb chops evenly. Cover the bowl with plastic wrap and set aside in the refrigerator overnight to marinade.
Add the water, salt, sugar, vinegar, and rice together into a large pot with a lid. Bring the mixture to a low simmer, cover the pot, and cook the rice for 10-15 minutes until tender. Fluff the rice with a fork and let it sit in the covered pot.
Preheat a large cast iron skillet over medium-high heat. When it begins to smoke, add the lamb chops to the pan. Cook for 3-4 minutes per side. Set aside.
Add the mint and green onions to the rice. Toss to combine. Add the rice to a serving bowl. Place the lamb chops on top of the rice and serve. Garnish with additional green onions, if desired.