Step 1: Make the Strawberry Filling
In a small saucepan, whisk together the sugar and cornstarch. Add the strawberries and lemon juice, stirring to mix. Cook over medium-low heat, stirring frequently until the berries soften and release juices, then mash them. Continue cooking until the mixture thickens to a jelly-like consistency. Remove from heat, stir in the butter, and refrigerate in a heatproof bowl.

Step 2: Prepare the Cookie Dough
Cream the softened butter and sugar in a large bowl with an electric mixer for about 1 minute until fluffy. Add the eggs and vanilla, stirring until combined. In a separate bowl, whisk together the cake flour, cornstarch, baking powder, baking soda, and salt. Gradually mix the dry ingredients into the wet ingredients until combined. Cover and chill for 30-60 minutes.

Step 3: Assemble the Cookies
Remove the dough and filling from the refrigerator. Scoop 1/4 cup (85g) of dough, divide it into two halves, and form each into a shallow nest. Place 2 teaspoons of filling into one nest, cover with the other, and pinch the edges to seal completely. Gently roll between your palms to create a smooth ball.

Step 4: Freeze Before Baking
Place the stuffed cookie dough balls onto a plate or baking sheet and freeze for 10-15 minutes. This step is crucial to ensure the cookies hold their shape.

Step 5: Bake the Cookies
Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper. Arrange the chilled dough balls 2 inches apart. Bake on the center rack for 14-16 minutes until the edges are light golden brown. Allow to cool completely on the baking sheet.

Step 6: Glaze and Serve
Whisk together the powdered sugar, 1 tablespoon of milk, corn syrup, and vanilla in a small bowl. Add more milk if needed to reach a spreadable consistency. Spread over the cooled cookies and top with sprinkles. Let the glaze harden before serving.