Heat oven to 425F / 218C.
Place potatoes in a saucepan and cover with cold water and some salt. Cover and bring to a boil. Remove lid from potatoes and simmer until potatoes can be easily pierced with a fork, 12 to 15 minutes.
Meanwhile, toss green beans with olive oil, mustard (portion for green beans), and balsamic vinegar. Season with some salt and pepper and spread out on a sheet pan. Roast until tender, shaking the pan halfway through cooking, 18 to 20 minutes.
Once green beans are roasting, heat a large skillet with cooking oil over medium heat. Add seitan and sear on all sides until golden, 6 to 8 minutes.
Add butter (portion for seitan) to pan with seitan. When butter melts, add shallots and tarragon. Saute until shallots are soft, 2 to 3 minutes. Stir in apple cider vinegar and mustard (portion for seitan).
Add flour to seitan and stir until no dry spots remain. Slowly pour in stock while whisking. Simmer sauce until thickened, 2 to 3 minutes. Season with some salt and pepper. Set aside, covered to keep warm.
Drain potatoes and let sit in a colander for ~5 minutes to allow the steam to escape (this creates creamier potatoes vs. liquidy potatoes).
Use a masher to mash potatoes with sour cream, butter (portion for potatoes), and some salt.
Serve seitan and sauce over mashed potatoes. Enjoy green beans on the side.