Melt butter in a large skillet over medium heat. Cook and stir couscous in the melted butter until slightly toasted, 2 to 3 minutes.
Pour in chicken broth and bring to a boil. Reduce heat to low and simmer until most of the stock is absorbed and the couscous have plumped, 6 to 7 minutes.
Stir heavy cream and pimientos into couscous; add cayenne pepper and cook until couscous is tender, 2 to 3 minutes. Add more broth if needed.
Remove from heat and stir in Cheddar cheese until melted; add chives and stir to combine. Season with salt, black pepper, and cayenne pepper to taste.
