Heat the olive oil in a large skillet over medium heat and add the fennel wedges. Season with salt and pepper and sear the fennel gently. As the fennel begins to brown, turn the wedges over and scatter in the sliced shallots. Cook until the shallots are tender, 2 to 3 minutes. Add the vermouth and cook until reduced by half, about 5 minutes. Add the chicken stock and simmer until the fennel is tender, 5 minutes. Add the reserved shallots and the mustard greens and stir until the greens have wilted, about 5 minutes. Add the croutons and toss to coat them with fennel and shallot juices.