For the dough: Mix the dry ingredients in a large bowl. Add the oil and water and mix well until the dough gathers into a ball, adding a little extra flour if it is sticky or a drizzle of water if dry. Knead for about 5 minutes until it becomes smooth and pliable. Lightly oil the bowl and turn the round dough over to coat. Cover with plastic wrap and let rest in a warm place for at least 2 hours.
For the topping: Combine all of the ingredients in a bowl.
To make man’oushe: Line 3 baking sheets with parchment paper. Divide the dough into 2 equal parts. Roll out half of the dough on a lightly floured surface to 2 mm thickness. Cut out the dough into rounds using a 10-cm round-shaped pastry cutter. Place the rounds on the lined baking sheet; press your fingers lightly onto the dough and spread with 1-heaped tablespoonful filling.
Preheat oven (220°C, 425°F). Bake on middle rack for about 12 minutes. Serve hot or lukewarm.