Melt the butter 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 on both sides, lay in the pan and fry four minutes. Flip, and cover to finish, four to six minutes. Serve with some brown butter dribbled over.
Spoon a small pile of the crushed chickpeas and olives on the plate. Add the fish to the plate and top with roasted carrots.
Heat oven to 400°F/200°C. 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, salt and pepper. Roast until tender and golden-edged, about 30 minutes, depending on their size. They should be slightly crinkly and golden-edged.
Soak the chick peas in a bowl of cold water over night. Drain and rinse, then put in a pot with the onion and bay leaf. Cover, just, with water. Bring to a simmer and cook, covered, until very tender, about 45 minutes. Drain, discarding the onion and bay leaf.
Heat the oil in a sauté pan and gently fry the garlic, 30 seconds. Add the chickpeas, salt, and pepper, to heat through. Crush a bit, here and there, with a potato masher, leaving some chick peas 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 fish or chicken.