Preheat the oven to 350°F (175°C).
Place a large skillet over medium-high heat. Add half of the oil. When shimmering hot, add half of the cabbage wedges, cut-side down. Sear until the side touching the pan is golden brown, 3 to 4 minutes. Flip and repeat on the other cut side. Transfer to a large, shallow baking dish. Repeat with the remaining oil and cabbage wedges. Season with salt and pepper.
Return the skillet to medium-high. Add the broth, thyme, and garlic powder. Bring to a boil, then reduce the heat and simmer for 5 minutes.
Pour the seasoned broth from the skillet over the seared cabbage in the baking dish, cover with aluminum foil, and bake until the cabbage core is fork-tender, about 30 minutes. Remove the cabbage wedges to a platter, cover loosely with foil to keep warm, then reserve the braising liquid in a bowl.
Using the same skillet, melt the butter over medium heat. Add the shallot and cook, stirring occasionally, until softened and a bit golden, 2 to 3 minutes. Stir in the reserved braising liquid, bring to a boil over high heat, and let the liquid reduce by about half, stirring and scraping often, 4 to 5 minutes. Turn the heat to medium/medium-high, stir in the mustard and the heavy cream and let simmer, stirring often, until the sauce reduces by half, 4 to 5 minutes. Season to taste with salt and pepper.
Pour the sauce over the cabbage wedges and serve.