Preheat the oven to 425 degrees . In a medium saucepan, bring 1-1/2 cups broth to a boil. Add the cauliflower, lower the heat, cover and simmer until fork-tender, 8 to 10 minutes. Using an immersion or standing blender, puree the mixture. Season to taste with salt.
While the cauliflower is cooking, heat the olive oil in a large, ovenproof skillet over medium-high heat. Season the pork chops with salt and pepper, add to the skillet and cook until browned, about 2 minutes. Flip and cook for 1 minute more. Place the skillet in the oven and roast the chops until an instant-read thermometer registers 145 degrees , 6 to 8 minutes. Transfer the chops to a cutting board and loosely tent with foil.
Return the skillet to high heat and add the remaining 1 cup broth and the vinegar, scraping up any browned bits from the pan. Cook, stirring, until the mixture is reduced by half, about 5 minutes. Stir in the figs and thyme. Add the butter, stirring until melted.
Divide the cauliflower puree and pork chops among 4 plates and spoon the fig sauce on top.