In a food processor, and blend until fine. Add the flour, butter and sugar. Mix until the contents resemble crumbs. Add the water (and the lavender if you are using it) 1 tablespoon at a time until a dough forms.
Remove from the food processor and roll into a ball. Wrap in plastic wrap and flatten to a disc. Refrigerate for about 30 minutes.
While the dough is chilling, preheat the oven to 350 degrees.
Place the cherries, lychee and sugar in a saucepan and heat on medium until the fruit releases its juices and begins to thicken. Set aside.
Roll out the dough until it is about ¼ inch thick. Cut out circles (I used a glass cup that is approximately 3 inches in diameter).
Place a dollop (about 1 - 1 ½ tablespoons) of the cherry-lychee mixture in the middle of each circle and pinch the outside of the dough to form a triangle.
Place on a baking sheet lined with parchment paper and bake for about 15 minutes, or until golden brown.
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