In a large sauté pan over medium heat, melt the ghee.
Add the onion, garlic, and ginger, and sauté, stirring, until fragrant, about 2 minutes.
Add the Brussels sprouts, and turn the heat up to mediumhigh.
Stir the Brussels sprouts so that all sides are covered with ghee, and then leave them to caramelize on one side.
Mix the sprouts around so the other sides make contact with the hot pan.
Continue to cook until most of the sides are browned and starting to get crispy, about 15 minutes in total.
Remove from the heat, and drizzle with the sesame oil.
Stir one more time, garnish with the sesame seeds, and serve.