Put chickpeas in a large pot, add water to cover by 2 in., and soak overnight. (Or bring to a boil over high heat, then turn off heat and soak about 2 hours.) Drain.
Pulse half the chickpeas in a food processor with 1/4 cup fresh water until coarsely chopped. Pour into pot used for soaking. Repeat with remaining chickpeas, more water, and the chiles. Add broth, 1 cup water, the turmeric, ground cumin, and 3/4 tsp. salt to pot.
Cover and bring to a boil over high heat, then reduce heat and simmer until chickpeas are tender, stirring occasionally, 40 to 50 minutes. Meanwhile, cook onions in oil in a large frying pan over medium heat, stirring occasionally, until deep golden, 12 to 15 minutes. Remove from heat.
Stir broccolini into chickpeas, return to simmering, and cook until tender, about 12 minutes.
Stir mustard and cumin seeds and remaining 1/4 tsp. salt into onions and cook over medium-high heat, stirring, until cumin turns a shade darker, 2 minutes. Set aside about one-third of mixture and stir the rest into dal. Ladle dal and quinoa next to each other in bowls and top with reserved onion mixture. Add more salt to taste.