Melt the ghee in a large saute pan set over medium-high heat and then cook the ground lamb (season with salt and pepper) until it becomes nicely brown and crispy, about 8 to 10 minutes; drain excess fat if desired.
Add uncooked rice and stir until it gets well coated and starts to turn translucent, then pour in the stock and bring to a simmer. Stir, cover and let cook over low heat until the liquid is completely absorbed and the rice is fully cooked, about 15 to 20 minutes.
Kill the heat and let the rice rest for an additional 5 minutes, then delicately stir in the chopped pistachios and fresh mint.
Spread 1/4 cup of yogurt at the bottom of each serving plate and then spoon and spread the rice over the yogurt.
Garnish with more chopped fresh mint and serve with fresh cucumber slices, if desired.