For the potatoes: Preheat the oven to 350 degrees F.

Toss the potatoes with the olive oil and 1 tablespoon salt in a Dutch oven or 12-inch cast-iron skillet with a lid. Cover with the lid and roast until tender, 40 to 45 minutes.

Meanwhile, for the cowboy butter: Combine the shallot, garlic, sage, thyme, rosemary, paprika, garlic powder, onion powder, chili powder, cayenne and 1 teaspoon kosher salt and ½ teaspoon black pepper in a food processor. Process until the mixture forms a chunky paste, about 10 seconds. Spread the butter chunks evenly across the food processor, so that it will blend evenly. Pulse until the butter is fully incorporated, about 30 seconds. Scrape the butter onto parchment paper or plastic wrap, then roll it into a cylinder and wrap it tightly. Refrigerator until you are ready to use it (this can be done up to a day ahead).

Transfer the pan with the potatoes to a stovetop burner and heat over medium-high heat. Unwrap the cowboy butter and slice it into 1-inch-thick slices. Place the butter slices on top of the potatoes and let them melt into the hot potatoes. Once the butter mostly melts, use a metal spatula to toss the potatoes every few minutes until they are golden brown all over, about 10 minutes. Stirring too often will break up the potatoes and prevent browning. Let cool for about 10 minutes before serving.