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Make chickpea patties: In a 3- to 4-qt.
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pan, mix chickpea flour and dry seasonings.
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Gradually whisk in 2 1/2 cups water until smooth.
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Cook over medium heat, whisking often, until mixture begins to thicken, 3 to 5 minutes.
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Switch to a spoon and stir until mixture pulls away from pan bottom and mounds in center of pan, 4 to 6 minutes.
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Stir in parsley.
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Using an oiled spoon or fingers, evenly spread mixture in an oiled 9- by 13-in.
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pan.
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Let cool.
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Make mayo: Mix all ingredients together in a small bowl.
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Chill, covered.
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Make slaw: Whisk together vinegar, oil, salt, and pepper in a medium bowl, then gently stir in carrots and radishes.
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Now for the sandwiches!
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Preheat broiler and set a rack 4 inches from heat.
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Split rolls, leaving one side attached, and open up.
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Place rolls cut side up in a large rimmed baking pan; lightly brush tops with 1 tablespoons olive oil.
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Broil until golden, about 1 minute.
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Tip onto counter and drape with foil.
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Oil the baking pan.
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Brush chickpea mixture with 1 tablespoons olive oil; sprinkle with salt.
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Cut into 12 rectangles and set slightly apart in oiled pan.
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Broil until golden, 4 to 6 minutes.
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Turn patties over and broil until golden on second side, about 2 minutes.
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To assemble, generously spread mayo on cut sides of rolls.
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Place some salad greens on one side of each roll and top with some carrot slaw, then 2 chickpea patties.