Preheat your oven to 350°F (175°C).
Combine 1 ¼ cups vegetable broth, lentils, barley, and yeast extract in a large saucepan over medium heat. Let it simmer gently for about 30 minutes until the lentils and barley are tender.
In another saucepan, combine the remaining ¾ cup broth, diced carrots, chopped onion, and walnuts. Cook this over medium heat for 15 minutes or until the vegetables are softened.
Meanwhile, place chopped potatoes in a large pot, cover with salted water, and bring to a boil. Reduce the heat to medium-low and simmer until the potatoes are fork-tender, about 15 minutes. Drain and mash the potatoes.
In a small bowl, mix the flour and water until smooth. Stir this mixture into the carrot mixture, cooking until the sauce thickens.
Next, combine the carrot mixture with the lentil mixture. Stir to incorporate and season to taste with salt and pepper.
Transfer the vegetable-lentil mixture into a 2-quart casserole dish. Spread the mashed potatoes evenly over the top.
Place the dish in the oven and bake for 30 minutes, or until the mashed potatoes are lightly browned. Serve warm and enjoy!