For the chickpeas: Soak the chickpeas in a bowl of cold water overnight. Drain and rinse, then put in a pot with the onion and bay leaf. Cover the beans, just with water. Bring to a simmer and cook, covered, until very tender, about 45 minutes. Drain the beans, discarding the onion and bay leaf.
Heat the oil in a saute pan, and gently fry the garlic, 30 seconds. Add the chickpeas, salt, and pepper, to taste, to heat through. Crush a bit, here and there, with a potato masher, leaving some chickpeas whole. Remove from the heat, and stir in the olives, parsley, and lemon zest. Add lemon juice, to taste. Drizzle with extra-virgin olive oil, and serve as a base for the fish or chicken.
For the carrots: Preheat the oven to 400 degrees F.
Slice the carrots lengthwise, leaving a bit of green top attached, for looks. Toss on a baking sheet with the olive oil, crushed cumin seed, and salt and pepper, to taste. Roast until tender and golden-edged, about 30 minutes, depending on their size. They should be slightly crinkly and golden-edged.
For the halibut: Melt the butter in a saucepan, and cook until lightly brown and foaming. Add a squeeze of lemon juice, and set aside.
Heat the oil in a frying pan. Season the fish with salt, and pepper on both sides, place the fish in the hot pan, and fry 4 minutes. Flip, and cover to finish, 4 to 6 minutes. Serve the fish with some brown butter dribbled over.
For plating: Spoon a small pile of the crushed chickpeas and olives on the plate. Add the fish to the plate and top with the roasted carrots.