Pat the chicken thighs dry with a paper towel so the skin can crisp up properly in the pan. Season both sides generously with salt, pepper, and paprika. While the chicken sits, halve the baby potatoes so they'll cook evenly alongside it.
Heat the olive oil in your skillet over medium-high heat until it shimmers slightly. Place the chicken skin-side down and let it brown undisturbed for about 4 minutes. Flip and sear the other side for 2 to 3 minutes, then set the chicken aside on a plate.
In the same skillet, add the shallot and cook for about a minute until it softens. Stir in the butter, garlic, thyme, rosemary, and oregano, letting everything sizzle together. This step only takes a minute, but it builds the base flavor for your entire sauce.
Pour in the chicken broth first and scrape up any browned bits stuck to the pan. Add the heavy cream and Parmesan, stirring until the sauce turns smooth and slightly thickened. Taste it here and adjust the salt if needed before adding anything else.
Nestle the potatoes into the sauce, then place the chicken thighs on top, skin-side up. Spoon a little sauce over the potatoes so they're mostly submerged. This keeps everything cooking evenly once it goes into the oven.
Transfer the skillet to a 400°F oven and roast for about 30 minutes. Check that the chicken reaches an internal temperature of 165°F and the potatoes are fork-tender. If the potatoes need more time, cover the pan loosely and roast a few extra minutes.
Pull the skillet out of the oven and let it rest for 5 to 10 minutes before serving. This gives the chicken time to reabsorb its juices so it stays tender when you cut into it. The sauce will also thicken slightly as it cools for a minute.