Martha merges the popular Arabian Gulf dish known as thareed, a meat-and-vegetable stew served over thin, cracker-like bread called rgaag, with an American comfort food that's a dinnertime favorite—chicken pot pie.
In a large Dutch oven, heat 1 tablespoon ghee over medium-high. Season chicken well with salt and pepper. Cook, working in batches as necessary, until chicken is lightly browned, about 4 minutes. Remove from pan.
Add remaining 2 tablespoons ghee along with onions, garlic, and serrano to pot. Cook until very soft and translucent, about 10 minutes. Add carrot and turnips and cook until just tender, about 4 minutes. Add eggplant, zucchini, and tomatoes and season with salt and pepper. Cook until vegetables are tender and tomatoes begin to break down. Combine tomato paste, spice blend, and 2 cups water and add to pot. Cook until aromatic, about 2 minutes.
Return chicken and any juices to pot and bring to a boil. Reduce to a simmer and cook until thickened, and chicken and vegetables are tender, about 25 minutes. Let cool slightly. Stir in parsley and season with salt and pepper. Ladle into six (1 1/2-cup) shallow ramekins; let cool.
Roll out thawed puff pastry on a lightly floured surface to a 1/4-inch thickness. Cut out six circles that are 1/2 inch wider than ramekins. Cut vents in the center of each circle. Transfer puff pastry circles to a parchment-lined baking sheet and freeze for 15 minutes.
In a small bowl, whisk together egg, yolk, and 1 teaspoon water. Remove puff pastry circles from freezer. Top each ramekin with a puff pastry circle, crimping edges over sides to seal, and brush with egg wash. Transfer to refrigerator and chill for 20 minutes.
Meanwhile, preheat oven to 425 degrees. Transfer ramekins to a rimmed baking sheet. Bake until puff pastry is deep golden brown and filling is bubbling, 20 to 25 minutes.