Prepare the strawberries by removing the stems and cutting them in halves if they're small, or quarters if they're large.
In a saucepan, combine the prepared strawberries, sugar, and water. Place the pan over medium heat.
Stir the mixture regularly to ensure all ingredients are combined. As the sugar melts, the strawberries will release their juices within a few minutes.
Allow the mixture to simmer for 8-10 minutes, stirring occasionally. The strawberries will soften and begin to break down, though the process may take longer if the fruit is less ripe.
Once done, remove the saucepan from the heat and transfer the compote to a jar or container to cool.
Refrigerate the compote before serving. It can be stored in an airtight container for up to 7 days.
Cream Cheese Filling:
In a medium-sized bowl, use an electric hand mixer to cream the room-temperature cream cheese until smooth and creamy, about 2 minutes.
Scrape down the sides of the bowl and add granulated sugar. Continue to cream for 1 more minute.
Add the beaten egg yolk and beat for an additional 30 seconds. Place in a piping bag and let it sit in the fridge while you make the cookie dough.
Cookie Dough:
In a medium-sized mixing bowl, whisk together all-purpose flour, cake flour, baking powder, salt, cornstarch, and ground cinnamon.
In a stand mixer fitted with a paddle attachment, cream slightly cold butter, light brown sugar, and granulated sugar on medium-high speed until light and fluffy, about 4 minutes.
Add the whole egg and mix on medium speed for 30 seconds. Scrape down the sides and bottom of the bowl, then add the half egg yolk and vanilla. Mix for an additional 30 seconds.
On the lowest speed, add the dry ingredients to the wet ingredients just until no streaks of flour remain. Avoid overmixing.
Divide the dough into 14 equal balls, I used a 3 tablespoon size cookie scoop. Roll each ball in your palms to form a smooth ball.
Press the back of a spoon or a tablespoon into the center of each cookie to create a shallow well. Pipe the cream cheese filling into the bottom of the well and spoon the strawberry filling into the other half.
Chill the dough balls in the fridge for 1-2 hours or overnight.
Preheat the oven to 375°F (190°C). Line two cookie sheets with parchment paper.
Place 4 cookie dough balls on each prepared cookie sheet, spacing them apart.
Bake for 13-15 minutes or until the cookies are lightly golden around the edges.
Allow the cookies to cool slightly on the cookie sheets before transferring them to a wire rack to cool completely.