Prep the sorrel chive butter by finely chopping the sorrel leaves and fresh chives. Mix into the softened butter with a fork. Season with ½ teaspoon kosher salt and ¼ teaspoon of ground black pepper. Set to the side.

Bring a large saucepan filled with water to a boil. Prepare an ice bath in a large mixing bowl for blanching the new potatoes and green beans.

Once water is boiling, add the potatoes and boil for 3 to 5 minutes until they become just knife tender. They will cook relatively quickly so keep an eye on them. Use a slotted spoon to remove potatoes promptly and place them in the ice bath. Remove potatoes to dry on a rimmed baking sheet lined with unbleached paper towels or clean linen kitchen towel to remove excess moisture.

Add the green beans to the boiling water and cook for 1 to 3 minutes until they turn a bright green. Use a slotted spoon to remove green beans promptly and place them in the ice bath. Remove green beans to dry on a rimmed baking sheet lined with unbleached paper towels or clean linen kitchen towel to remove excess moisture.

Preheat a large cast iron skillet over medium heat. Add 1 tablespoon olive oil and swirl to coat bottom of pan. Add the new potatoes and cook, stirring frequently, until the edges begin to crisp and potatoes begin to turn slightly golden, about 5 to 7 minutes. During the last two minutes of cooking, add the blanched green beans. Season with the remaining kosher salt and ground black pepper. Spoon in the prepared sorrel chive butter and stir to coat the green bean and potatoes in the compound butter.