Preheat broiler. Cut the stems off each fig, slice the figs in quarters and set aside.
Add the butter, brown sugar and honey to a cast-iron pan or medium broilerproof saute pan. Cook for about 1 minute over high heat, stirring frequently, until the syrup begins to bubble. Add the figs and stir to coat them with the syrup.
Place the pan under the broiler to caramelize the figs. Protecting your hand with an oven mitt, swirl the pan a few times over the next five minutes to prevent the sugar and figs from burning. The figs are done when the syrup is thickened slightly and amber in color, and the edges of the figs are dark and glossy. Remove the pan from the broiler and serve.
This jammy compote was designed to be poured over porridge, but is equally good atop pancakes, waffles or frozen yogurt.