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Step 1
Heat the oven to 500°F. Stir 4 tablespoons melted unsalted butter, 1 teaspoon of the kosher salt, and 1/8 teaspoon cayenne pepper together in a large bowl. Add 2 pounds peeled and cut Yukon gold potatoes and toss well to coat.
Step 2
Transfer the potatoes cut-side up to a 9x13-inch metal baking pan (avoid glass, as it could shatter) or 9x13-inch rimmed baking sheet (quarter sheet pan) and arrange in a single layer. Drizzle any remaining butter mixture over the potatoes.
Step 3
Roast until the potatoes easily release from the pan with tongs and the bottoms are golden-brown, about 15 minutes. Flip the rounds and roast until the bottoms and tops are deep golden-brown, 10 to 12 minutes.
Step 4
Meanwhile, whisk 1 cup low-sodium vegetable broth, 1 tablespoon lemon juice, 2 teaspoons prepared horseradish, 1 1/2 teaspoons Dijon mustard, 1 teaspoon smoked paprika, and the remaining 1/4 teaspoon kosher salt in a liquid measuring cup until combined.
Step 5
Remove the pan from the oven. Carefully pour the broth mixture into the pan and add 4 peeled and smashed garlic cloves. Return to the oven and roast until the potatoes are very tender and most of the broth is absorbed, about 15 minutes. Flip the potatoes and garnish with finely chopped fresh parsley leaves before serving.