Combine raspberries, water, and sugar in a small saucepan. Simmer for 10 minutes.
Mix corn starch with cold water and slowly add to the simmering raspberry mixture, stirring continuously.
Cook until the mixture thickens, resembling pie filling.
Transfer to a glass bowl and let it cool for at least 30 minutes, stirring occasionally.
To prepare the cookie dough:
Cream together butter and brown sugar until smooth.
Add the egg and vanilla extract, mixing well.
Sift flour and baking powder together, then fold into the creamed mixture to form a soft dough.
Divide the dough into two equal parts.
Line a 9x9 inch baking pan with plastic wrap and press half the dough into the bottom. Lift it out using the plastic wrap and chill.
Grease the baking pan lightly and line with parchment paper. Press the remaining dough into the bottom of the pan, smoothing it with the back of a spoon.
Evenly spread the cooled raspberry filling over the base dough layer.
Place the chilled dough square on top of the filling, peel off the plastic wrap, and gently press to remove air pockets.
Bake at 350°F for 25-35 minutes until the top is lightly golden.