Add 2 tablespoons butter to a cast-iron skillet over high heat and add the endives cut-side down. Sear until the bottoms are slightly charred, then add the remaining 4 tablespoons butter along with the chestnuts and sage leaves and cook until the chestnuts begin to brown. Finish with the sherry vinegar and season with salt and pepper. Remove from heat.
Arrange the endives on a plate or platter charred-side up. Spoon chestnuts over the endives, then drizzle with the sauce. Serve immediately.
This recipe has been updated and may differ from what was originally published or broadcast.