Preheat the oven to 375°. Whisk the eggs, turmeric, and a pinch of salt in a large bowl.
Heat 2 tablespoons oil in an 8- to 10-inch cast-iron or ovenproof nonstick skillet over medium heat. Add the onion and a pinch of salt. Cook, stirring occasionally, until translucent, about 5 minutes. Add the chard, 2 cups at a time, folding after each addition to wilt. The whole process will take about 5 minutes. Add the parsley and a large pinch of salt and stir well. Scrape all the vegetables into the bowl with the eggs.
Add the remaining 2 tablespoons oil to the skillet and swirl to coat the bottom and sides evenly. Stir the egg mixture to distribute the greens evenly, then pour into the hot skillet. Spread in an even layer. When the edges begin to bubble, transfer to the oven.
Bake until just set, about 10 minutes.
Scatter the barberries, pistachios, and mint on top. Cut into wedges to serve hot, warm, or at room temperature.
Recipe by Genevieve Ko.