Stir together butter, garlic, mixed herbs, mustard, lemon zest and lemon juice, smoked paprika, black pepper, thyme, chili powder, crushed red pepper, and 1 teaspoon of the salt in a bowl until well combined.
Transfer half of the butter mixture to a small bowl, cover, and refrigerate until mixture firms up, about 30 minutes.
Preheat the oven to 500 degrees F (260 degrees C); position a rack in the upper third of oven.
Toss potatoes, oil, and remaining 1/2 teaspoon salt in a bowl with remaining 1/4 cup butter mixture until potatoes are evenly coated. Arrange in a single layer in a 9-by-13-inch metal baking pan, scraping any leftover butter mixture from bowl over potatoes. (Don’t use a glass dish, which could shatter.)
Roast in the preheated oven, flipping once using a spatula, until browned, about 30 minutes.
Carefully add broth to the pan. Continue roasting at 500 degrees F (260 degrees C), undisturbed, until potatoes are very tender and most of the liquid is absorbed, about 8 minutes.
Remove from the oven. Immediately add remaining cold butter mixture, a spoonful at a time, carefully swirling the pan until butter is fully melted and emulsified. Evenly sprinkle with chopped herbs. Serve with lemon wedges.
