Coat an 8- or 9-inch baking dish with cooking spray and line with parchment paper, leaving an overhang on either side. Set aside.
Preheat the oven to 375 F.
Prepare the shortbread: In a spice grinder or small food processor, process freeze-dried strawberries to a powder (a few larger pieces are okay).
In the bowl of a stand mixer fitted with a paddle attachment, beat to combine butter and sugar until smooth.
Add food coloring (if desired), strawberry powder, 1 cup of flour, and salt. Beat until a crumbly dough forms.
Transfer shortbread to the prepared dish and press evenly to cover the bottom, then set aside.
Prepare the brownies: In a small bowl, whisk to combine remaining flour, cocoa powder, salt, and baking powder.
In a small pot, melt the butter.
Remove butter from heat, add chocolate, and stir until smooth.
In a medium bowl, whisk to combine eggs and sugar for 2 to 3 minutes until lightened and frothy.
Whisk in vanilla and chocolate mixture.
Fold in dry ingredients until smooth.
Fold in ½ cup white chocolate chips.
Pour batter evenly over shortbread base.
Lay sliced strawberries evenly over the top of the brownie batter in a single layer. Sprinkle with flaky sea salt if desired.
Bake for 50 to 55 minutes or until a wooden pick inserted in the center comes out mostly clean with a few fudgy bits. Transfer to a wire rack to cool completely. If you have time, chill for at least 1 hour or until firm before cutting.
Lift brownies out of pan using parchment paper and transfer to a cutting board, removing parchment.
Melt remaining ¼ cup white chocolate and drizzle it over the top of the brownies.
Trim the edges of the brownies and cut into 16 squares.
Serve the chocolate strawberry brownies. Store leftovers in an airtight container in the refrigerator for up to 5 days.