Cut a piece of parchment paper to fit, with much excess, an 8-inch square baking pan. Don't attempt to fit the paper in just yet.
Place a rack in the center of the oven. Preheat the oven to 400°F.
Beat the eggs with the vanilla and sugar with a fork in a large mixing bowl. Add the dates and walnuts and mix well. Sprinkle the flour over the fruit and nut mixture and blend in very well.
Place the parchment paper over the pan and pour the batter into the pan. The weight of the batter will hold down the paper. As you spread the batter to fill the pan, the paper will give way and fit to the pan more snugly.
Bake for about 45 minutes until the top is nicely browned and the cake feels solid to the touch.
Place the cake on a cake rack and let cool for 20 minutes. While the cake is still warm, unmold it, leaving the paper-lined side up, and let cool a little longer.
Carefully pull of the parchment paper while the cake is still warm. Finish cooling the cake with the sticky bottom up. Use a serrated-blade knife to cut the cake into approximately 1 1/2-inch squares. Or cut into 1-inch by 2-inch bars or, truly, into any size you like.
The cake can be served warm, when it is particularly good with whiiped cream or a scoop of ice cream. Or serve at room termperate. It improves with a few days of age.
Store at room temperature, in a tin or wrapped in aluminum foil, not plastic.