In a 10-inch deep skillet, heat the oil. Add the lemon, shallot, celery and carrot and cook, stirring occasionally, for 10 to 12 minutes until softened.
Add the turmeric, fennel, chili flakes, black pepper, a big pinch of salt and cook for 1 minute, until fragrant.
Add the flour, and cook, stirring to coat for 1 to 2 minutes until toasty.
Add the rosemary or thyme, stock, coconut milk, lemon juice, sugar, stir constantly and bring to a boil. Reduce the heat and simmer for 8 to 12 minutes, until slightly thickened. Taste and season with more salt as needed. Take out the herbs.
Stir in the cooked chicken and set aside to cool a little bit.
Heat the oven to 400°F.
Lightly flour your work surface to prevent the pastry from sticking. Roll the puff pastry to ¼ inch thick. Cut out a circle bigger than the skillet, about 12-inches in diameter.
Place the pastry on top and crumple the edges. Slice a few holes in the center to let the steam escape.
Top with lemon slices for decoration, and brush olive oil on top.
Bake for 30 to 35 minutes, until the pastry is nicely puffed and golden. Serve right away.
