Heat oven to 400 F (200 C).
In cake or casserole pan, place beets and add enough water so that it covers the bottom 1 in (2.5 cm) of beets. Cover pan with parchment paper, place in oven, and bake for 35 minutes, or until beets are fork-tender. When cool enough to handle, rub beet skins off with paper towel. Slice beets into 1 in (2.5 cm) wedges.
In medium saucepan, place lentils, bay leaf, a couple pinches of salt, and 2 cups (500 mL) water. Bring to a boil; reduce heat to medium-low and simmer, covered, until lentils are tender but still have some bite, about 25 minutes. Drain any excess liquid.
In separate saucepan, place quinoa, a couple pinches of salt, and 1 1/2 cups (350 mL) water. Bring to a boil, reduce heat to medium-low and simmer, covered, until quinoa is tender and liquid has absorbed, about 13 minutes. Remove from heat and let stand, covered, for 5 minutes. Fluff with fork.
To make dressing, place steamer basket in pot with 1 in (2.5 cm) water. Place carrot in basket, cover, and steam until carrot is fork-tender. In blender container, place carrot, 2 Tbsp (30 mL) of the carrot steaming water, olive oil, vinegar, miso, ginger, and sesame oil, if using, and blend until as smooth as possible. Add more water if needed to help with blending.
To serve, divide arugula or dandelion greens among serving plates and top with lentils, quinoa, beets, avocado, mint or dill, feta, pumpkin seeds, and dried cherries. Drizzle on carrot dressing.