Preheat the oven to 425 degrees. Toss the carrot sticks with 1 tablespoon olive oil, 1/2 teaspoon cumin, and a pinch of salt on a baking sheet. Roast for 20 minutes until the edges start to brown.
While the carrots roast, mix the remaining cumin, coriander, cinnamon, paprika, salt, and pepper in a small bowl. Rub the lamb chops with 1 tablespoon olive oil and the spice blend on both sides.
Heat the remaining tablespoon of olive oil in a large skillet over medium-high heat. Cook the lamb chops for 3 to 4 minutes per side until they reach your preferred doneness. Remove them from the pan and let them rest.
Bring the vegetable broth and minced garlic to a boil in a small saucepan. Stir in the couscous, cover, and remove from heat. Let it sit for 5 minutes, then fluff with a fork.
Divide the couscous among four plates. Add the roasted carrots and two lamb chops to each plate. Scatter fresh mint leaves over the top before serving.