In a small saucepan, combine rinsed quinoa and water. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes until water is absorbed. Remove from heat and let stand covered for 5 minutes, then fluff with a fork.
In a food processor, combine chickpeas, parsley, cilantro, onion, garlic, cumin, coriander, salt, and pepper. Pulse until well combined but not pureed—mixture should be slightly chunky. Transfer to a bowl, stir in flour and baking powder until a dough forms. Cover and refrigerate for 15 minutes.
Heat 1 inch of vegetable oil in a large skillet over medium-high heat (350°F/175°C). Shape the falafel mixture into 16 small balls or patties (about 1.5 tablespoons each). Carefully place in hot oil and fry in batches, turning occasionally, until golden brown and crispy, about 4-5 minutes total. Drain on paper towels.
While falafel cooks, dice the cucumber and shred or ribbon the carrots. If using store-bought pickled onions, drain them. If making quick pickled onions, slice 1 small red onion thinly, toss with 1/4 cup apple cider vinegar, 1/2 cup warm water, 1 tsp sugar, and 1/2 tsp salt; let sit 10 minutes.
Divide the cooked quinoa among 4 bowls. Arrange falafel, diced cucumber, shredded carrots, a generous dollop of hummus, a drizzle of tahini sauce, and a pile of pickled onions in neat sections. Garnish with fresh parsley. Serve immediately.