Preheat the oven to 425 degrees . Roll out the puff pastry into a 12-inch square. Set aside four 2-cup bowls; invert 1 bowl onto the pastry and cut out 4 rounds. Place on a parchment-paper-lined baking sheet and brush with the egg. Sprinkle with the poppy seeds and bake until golden, 12 minutes. Let cool.
In a large saucepan, add the potatoes and enough water to cover. Bring to a boil, salt the water and cook until tender, 7 minutes. Add the peas and cook for 1 minute; drain.
In a skillet, heat 2 tablespoons EVOO over medium heat. Add the chicken, season with salt and pepper and cook for 7 minutes. Transfer to a plate. Add the remaining 1 tablespoon EVOO to the skillet. Add the leeks and carrot; season with salt, pepper and the thyme. Cook for 3 minutes.
Scoot the leeks to the side and add the butter. Whisk in the flour, then the wine and chicken broth. Stir in the chicken and cream and heat through. Stir in the lemon peel, lemon juice, potatoes and peas. Fill the bowls with the chicken mixture and top with the crust.