Begin by preparing the prunes. Remove the pits and chop the prunes into small pieces.
In a small saucepan, place the chopped prunes and cover them with water. Simmer over low heat until the prunes are soft and tender. This should take about 10-15 minutes. Once cooked, remove from heat and allow them to cool.
Mash the cooked prunes with a fork or blend them until you achieve a smooth, jam-like consistency. Set aside.
Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a mixing bowl, cream together the softened butter and granulated sugar until the mixture is light and fluffy.
Add the eggs, one at a time, beating well after each addition. Then, add the vanilla extract and lemon zest, mixing until well combined.
In a separate bowl, whisk together the all-purpose flour, baking powder, and salt.
Gradually add the dry ingredient mixture to the wet ingredients, mixing until a dough forms. The dough should be soft and slightly sticky.
Take a portion of the cookie dough and flatten it in your hand. Place a teaspoon of the prepared prune filling in the center of the dough.
Fold the dough over the filling, sealing the edges well. Shape the dough into a round or oval cookie shape.
Place the filled cookies onto the prepared baking sheet, leaving some space between each cookie.
Bake in the preheated oven for about 12-15 minutes, or until the cookies turn golden brown around the edges.
Remove the cookies from the oven and allow them to cool on a wire rack before serving.