Place the figs and dates in a saucepan and cover with water 1 inch above the fruit.
Bring to a boil and reduce the heat. Simmer until tender, about 20 minutes. Drain.
Place the fruit on paper toweling for 10 minutes to blot up any excess water.
Process the fruit, sugar, lemon zest, and cognac with the steel blade in a food processor until a smooth paste forms.
Preheat the oven to 350. Cream the butter and brown sugar together in a large mixing bowl.
Add the eggs, one at a time, beating well after each addition. Add the vanilla and combine well.
Stir in the oats; flour baking powder, cinnamon, and salt. Add the chopped hazelnuts.
Pat two-thirds of the oatmeal mixture in the bottom of a 9-inch square baking pan.
Spread the date-fig puree over the oatmeal. Crumble the remaining oatmeal with your fingers and sprinkle it loosely on top of the fruit puree.
Bake for 25 to 30 minutes. Cool completely. Cut into 16 squares.