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1
Heat 2 cups of the canola oil in a medium saucepan over medium heat until it reaches 360F on a deep-fat thermometer.
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2
Fry the pita slices, in batches, until lightly golden brown and crisp, turning once, about 1 minute.
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3
Transfer with a slotted spoon to a plate lined with paper towels and season with salt and pepper.
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4
Preheat a grill to high or heat a grill pan over high heat.
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5
Brush the asparagus with the remaining 2 tablespoons oil and season with salt and pepper.
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6
Grill the asparagus, turning once, until crisp-tender, 4 to 6 minutes.
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7
Transfer to a cutting board and cut on the bias into 1-inch-long pieces.
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8
Combine the mesclun, tomatoes, cheese, cucumber, olives, chickpeas, and asparagus in a large bowl.
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9
Add half of the dressing, season with salt and pepper, and toss well to coat.
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10
Divide the salad among large dinner plates.
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11
Drizzle with more of the dressing and top with the pita chips.
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12
Whisk together the lemon zest and juice, vinegar, mayonnaise, mustard, and honey in a medium bowl.
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13
Season with salt and pepper.
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14
Slowly whisk in the oil until emulsified.
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15
The dressing can be made 1 day in advance and stored in a container with a tight-fitting lid in the refrigerator.
