Over medium-high heat, melt the butter in a large sauté pan. Add in the Brussels sprouts and cook just until they turn a vibrant green, about 3-5 minutes, stirring only occasionally to allow edges to brown. Add in the pomegranate honey and the salt. Stir to coat the sprouts, and then pour in the pecans.
Remove from heat and stir in the pomegranate arils. Serve warm.
To make the pomegranate honey, reduce 1 cup pomegranate juice by half over medium-high heat. Add in 1/4 cup honey and simmer until thick. Full instructions can be found on FoodforMyFamily.com.