In a medium bowl, cream the butter until light and fluffy. Add the sugar, and mix until lightened in color and no longer grainy looking. Add the egg and vanilla, and mix until incorporated. Add the flour and mix just until combined.

Fill a small bowl half full with water and keep ready.

Drop spoonfuls (about 2 tsp) of batter onto a nonstick baking sheet, spacing them about 2" apart from the other spoonfuls. Dip your finger into the water, and use to spread each spoonful into a flat circle about 2" in diameter. Make a slight divot in the center. The dough is pretty sticky, so don't be afraid to keep wetting your finger.

Bake at 350F for 7-8 minutes. Let the cookies cool slightly on the baking sheet, then transfer to a wire cooling rack to cool completely.

Match the cookies up by size, so each has a friend. Dollop a spoonful on the flat side of one cookie, and smoosh its friend on top, flat side down into the filling, until the filling almost starts to spill out. The cookies will start to soften once they're sandwiched, so wait until the last moment before filling.

In a food processor, grind the fruit and sugar until powdery and fine. If you notice some clumps that refuse to pulverize, strain or pick out those pieces. Add the cream and stir with a fork to ensure that there are no dry pockets of powder, then pulse until thick and creamy like Greek yogurt, less than 2 minutes. The time will vary depending on your machine, so watch carefully to stop it before you make butter (though there are worse things than strawberry butter). Use immediately or refrigerate up to 1 week.