Preheat the broiler. Toss the parsnips and turnips in a large bowl with 1 tablespoon olive oil, 1 teaspoon ras el hanout, 1/4 teaspoon salt and a few grinds of pepper. Spread on a baking sheet and add the lemon halves cut-side up. Broil until the vegetables are lightly browned, about 5 minutes.
Toss the chickpeas in the same large bowl with 1 tablespoon olive oil and the remaining 1 teaspoon ras el hanout. Add to the baking sheet with the other vegetables and stir. Broil until tender, about 5 minutes. Let cool 5 minutes.
Squeeze the juice from the broiled lemon into a large bowl. Add 1/4 teaspoon salt and a few grinds of pepper, then whisk in the remaining 1/4 cup olive oil. Add the chicken, dried apricots, olives and almonds and toss to coat. Add the broiled vegetables and chickpeas and arugula-spinach blend; toss.