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1
Preheat the oven to 400 degrees. Have a large baking sheet at hand.
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2
Mince the garlic with a pinch of salt; use the flat blade of a chef's knife to work the garlic so it softens and breaks down. Cut the onion in half, then into very thin half-moons. Stem and de-rib the bell pepper, then cut the flesh into very thin slices. Finely chop the cilantro. Drain the chickpeas to yield about 4 cups.
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3
Heat the oil in a large skillet, preferably nonstick or well-seasoned cast-iron, over medium heat until the oil shimmers. Add the garlic, coriander and cumin; cook for 3 minutes, stirring, until the garlic is fragrant. Stir in the chickpeas, crushed red pepper flakes and 1/4 teaspoon of the paprika; cook for 8 minutes, stirring, until the chickpeas are coated and heated through. Drizzle lightly with oil (up to 1 tablespoon), then use a potato masher to mash about half of the spiced chickpeas so the mixture is nubbly and thickened. Stir in up to 1/4 cup water to make the mixture creamy.
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4
Meanwhile, place the nan on the baking sheet. Drizzle lightly with the oil. Warm them in the oven while the remaining vegetables cook; they will turn lightly golden.
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5
Use a spatula to shove the chickpea mixture to the edges of the skillet. Add the onion and bell pepper; cook for 3 or 4 minutes, until the onion has softened and the bell pepper is crisp-tender. Season with salt and pepper to taste. Stir in most of the cilantro and remove from the heat.
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6
Peel the cucumber half, if desired, then grate it on the large holes of a box grater to yield a scant 1 cup; place in a medium bowl, along with the yogurt and the remaining 1/4 teaspoon of paprika. Stir to form a thick sauce. Season with salt and pepper to taste.
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7
Place a warm nan on each plate. Spoon equal amounts of the chickpea mixture on each one, then top with some of the cucumber yogurt. If desired, drizzle each portion with a little oil. Sprinkle with the remaining cilantro. Serve warm.
