Place the butter and olive oil in a large cast-iron skillet over low heat. Add the halved baby potatoes and cover with a lid. Cook gently for around 15 minutes, stirring occasionally, until the potatoes are tender. Remove the lid for the last 4–5 minutes of cooking and increase the heat slightly, frying the potatoes until they are golden and crispy. Cook a little longer if needed to achieve the desired crispiness.