Whisk the chickpea flour, salt, pepper, turmeric, water, and two tablespoons of the oil in a medium bowl until smooth. Let the batter rest for 30 minutes — this ensures the flour hydrates properly for a tender interior.

Heat one tablespoon of oil in a 10-inch nonstick skillet over medium heat until the oil should shimmer but not smoke. Add the onion, garlic, cumin, allspice, salt, and pepper and cook until the onion is softened and translucent, about 5 minutes.

Stir in the chard and apricots. Cover and cook, stirring occasionally, until the chard is wilted and tender, 3 to 5 minutes. Stir in the pistachios and vinegar, then transfer the mixture to a bowl and cover to keep warm.

Wipe the skillet clean with paper towels. Heat one teaspoon of oil over medium-high heat until shimmering. Pour a generous half-cup of batter into the center of the skillet and swirl to coat the bottom completely. Cook until the edges are set and the bottom is deeply browned and crisp, about 2 to 3 minutes.

Carefully flip the flatbread and cook until the second side is browned and the center is cooked through, about 2 minutes. Transfer to a plate and repeat with the remaining oil and batter.

Divide the chard topping among the warm flatbreads and serve immediately, while the edges are still crisp.