Gather all ingredients. Preheat the oven to 350°F (175°C).

Combine 1 ¼ cups broth, lentils, barley, and yeast extract in a large saucepan over medium-low heat; simmer for 30 minutes.

Meanwhile, combine remaining 3/4 cup broth, carrot, onion, and walnuts in a medium saucepan over medium heat; cook until tender, about 15 minutes.

Place potatoes in a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender but still firm, about 15 minutes. Drain and mash.

Combine flour and water in a small bowl; stir into carrot mixture and simmer until thickened. Combine carrot and lentil mixtures; season with salt and black pepper.

Transfer carrot-lentil mixture to a 2-quart casserole dish; spoon mashed potatoes over top.