Place the potatoes in a small saucepan and cover with 1” water. Bring to a simmer over medium heat and cook until just tender, about 10 minutes. Drain and reserve.
While the potatoes cook, add the carrots, garlic cloves, butter, and chicken stock to a large sauté pan. Add a good pinch of salt, then cover pan and bring to a simmer over medium-high heat and. Cook until carrots begin to soften, about 5 minutes. Remove the lid and add the green beans and mustard. Cook uncovered, stirring occasionally until beans are tender and the chicken stock has reduced down to a buttery glaze, 5-10 minutes more. Add the drained potatoes and toss to combine. Taste for seasoning, then transfer to a serving plate and garnish with chopped herbs.