In a large bowl, whisk the flour, salt, and baking powder until combined. Add 1/2 cup yogurt and 1 Tbsp. lukewarm water. Use your hands to knead the dough together into a ball.
Place the dough on a lightly floured surface, and knead until smooth (dough will still be slightly tacky), about 2 min. Return to the bowl, and cover the surface with a towel or plastic wrap. Let sit at room temperature for 30 min.
On a lightly floured surface, divide the dough into 4 equal-size rounds. Using a rolling pin, roll 1 round into a very thin 8-in. circle, keeping the others covered.
Brush the top of the circle with 1 1/2 tsp. ghee. Sprinkle with 2 Tbsp. green onions and 1/2 tsp. sesame seeds. Starting from 1 end, roll the dough into a tight log, then twist the log into a tight spiral. Tuck the end under the spiral, and cover. Repeat with remaining rounds of dough.
Working with 1 spiral at a time, roll the spirals into 7-in. circles. (Keep covered when not using.) Cover, and let rest 30 min.
Heat 1 Tbsp. ghee in a medium heavy-bottom skillet over medium. Add 1 flatbread, and cook, flipping halfway, until golden brown on both sides and cooked through, 2 to 3 min. per side. Transfer to a paper towel-lined plate. Repeat with the remaining flatbreads and 3 Tbsp. ghee.
Place the chile and garlic on a cutting board. Sprinkle with salt, and smash into a paste with the side of a chef's knife. Scrape the paste into a medium bowl, and stir in the coriander, cumin, cardamom, arugula, oil, and lemon juice. Season with salt and pepper.
When ready to serve, spread remaining 1/2 cup yogurt on top of flatbreads. Season with salt and pepper. Top with eggs, zhug, and more sesame seeds.
Recipe by Laura Rege.