To the blender, add the persimmons with a couple of tablespoons of water. This may need to be done in batches depending on how large your blender is. Blend on high for 2-3 minutes or until completely smooth. Push the persimmon pulp through a sieve into a separate bowl. Set aside.
To a heavy bottomed large saucepan, add the persimmon pulp, water, lemon juice, sugar, honey, cinnamon, nutmeg and cloves. Cook over medium-low heat for 45 minutes to an hour, stirring occasionally, or until the jam just begins to clump. Transfer to jars and cover. Let the jam cool completely at room temperature and then transfer to the refrigerator where it will keep for about 2 weeks.
Preheat your oven to 350 degrees F and line two large cookie sheets with parchment paper or silicone baking mats. Set aside.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In the bowl of your stand mixer with paddle attachment fixed (or with a handheld mixer), cream together the butter and sugar until smooth. Add each egg yolk, one at a time, mixing after each addition. Then add the vanilla extract and beat again. With the mixer speed set on low, gradually add the dry ingredients to the wet until just incorporated.
Cover the bowl and place in the fridge for 20 minutes. Remove the dough from the fridge and roll the dough into tablespoon-sized balls. Place them on the prepared baking sheets. Gently press your thumb into each cookie to make an indent.
Bake the cookies for 12-15 minutes or until they just begin to brown along the edges. Remove from heat and press down again with your thumb or a spoon in case the indentations puffed up. Be careful, as the cookies are hot.
Let the cookies cool completely on wire racks before spooning the persimmon jam into each indentation.
Store the cookies at room temperature in an airtight container for 3-4 days. Enjoy!