In a small stainless steel skillet, heat butter over medium heat. Slice figs in half lengthwise and drizzle with honey.
Place honeyed figs cut side down into the skillet. Add the fresh rosemary sprig and pinch of flaky sea salt. Allow figs to cook undisturbed for 3 to 5 minutes.
Transfer figs to a plate and add 2 tablespoons of water to the pan to begin to scrape up any browned bits from the figs. Allow sauce to thicken slightly before pouring sauce over the caramelized figs.
Serve the figs atop ice cream, yogurt, or your morning oats.