Melt the butter in the skillet. Add the carrots and season them with salt. Cover the skillet and cook the carrots over moderate heat, stirring them occasionally, until they are barely tender, about 6 minutes. Add the vegetable stock to the carrots, cover the skillet partially and cook over moderately high heat, stirring the carrots occasionally, until they are tender and the liquid has reduced to a glaze, about 10 minutes longer. Stir the peperoncini mixture into the carrots and cook just until it is heated through, about 1 minute longer. Season the carrots and peperoncini with salt and pepper, transfer the vegetables to a bowl and serve.