Rinse the persimmons and remove the brown or green calyx. Place the strainer over the 2-quart bowl. One at a time, place a persimmon in the strainer and press down hard with the spatula. Press and move the spatula around, forcing the pulp through the mesh. Remove the seeds and skin and continue with the remaining persimmons. (Note: This can take a while when using small persimmons, so plan for it.)
Preheat the oven to 325° F/165° C. Set rack in the middle of the oven.
In the bowl of the stand mixer, cream the butter and sugar until it it light and fluffy.
Add the eggs, one at a time, beating well each time. Add the persimmon puree and vanilla extract, and mix well.
In the medium bowl, sift together the flour, cinnamon, nutmeg, and baking soda. Add to the butter mixture and stir gently, tossing in the chopped dates. Do not overmix.
Pour the batter into the prepared pan. Bake for 60 to 75 minutes, checking every 5 minutes after 1 hour has passed. When a tester comes out dry with just a few crumbs clinging, remove the pan from the oven. If the tester has no crumbs the cake will be dry.
Cool the cake in the pan for 15 minutes, then turn the cake out onto a wire rack and cool completely.
While the cake is cooling, whisk together the the powdered sugar and lemon juice until the glaze is smooth.
Pour the glaze over the cake while warm. Allow to cool completely, then slice and serve.