Prepare the strawberry compote.
In a medium saucepan, combine sliced strawberries, granulated sugar, cornstarch, and lemon juice. Cook over medium heat, stirring gently, for 5 to 7 minutes until mixture thickens and becomes glossy. Strawberries should hold their shape but be coated in thick, jam-like syrup. Remove from heat and let cool completely, at least 30 minutes.
Prepare for assembly. Preheat oven to 350°F (175°C). Line a large baking sheet with parchment paper. Get your 2.5 to 3 inch circle cutter or wide mouth canning jar ready.
Assemble the cookies.
Using your circle cutter as a guide, spread about 1 heaping tablespoon of fermented crumble mixture on the parchment in circles. Top each crumble circle with 2 teaspoons of cooled strawberry compote. Roll out the fermented cookie dough on a floured surface to a rough rectangle, approximately 1/4 to 1/2 inch thick. Using your circle cutter, cut out circles from the dough. Gently gather scraps, press together to form another rectangle, and continue cutting until all dough is used. Place each cookie circle on top of the crumble and strawberry layers. Gently press down to adhere.
Bake.
Bake for 18 to 22 minutes, until cookie tops are golden brown and set. Remove from oven and let cool completely on the baking sheet, at least 1 hour. The strawberry compote will continue to thicken and set as it cools. The cornstarch will firm up considerably during the cooling process, creating that perfect gel-like consistency that won't be sticky to the touch.
Add white chocolate drizzle.
Melt white chocolate with 1 to 2 teaspoons coconut oil in a microwave or double boiler until smooth. Using a spoon or piping bag, drizzle melted white chocolate over the cooled cookies.
Serve.
Once chocolate has set, carefully remove cookies from parchment using a thin spatula. Serve immediately or store covered for up to 3 days.