Preheat the oven to 475°F / 245°C convection (or 500°F / 260°C flat heat). Line an 8-inch / 20cm square cake pan with parchment paper that comes up the sides of the pan to act as a sling.
Make the crust: In a food processor, pulse to combine the cookie crumbs, brown sugar, butter, and salt. Pour the mixture into the prepared pan, cover with plastic wrap and press with a glass to an even layer.
Bake in the middle of the oven for 10 minutes, until it starts to look well toasted. Set aside to cool.
Make the fruit layer: In a small bowl, whisk together the sugar and cornstarch. In a small pot, cook the berries and sugar-cornstarch mixture together over medium heat until the juices are thick and clear, 3 to 5 minutes. Remove from the heat.
Make the cheesecake: In a stand mixer fitted with the paddle attachment, beat the cream cheese on medium speed for about 1 minute, until smooth. Scrape down the sides and mix for another 30 seconds. Add the sugar and mix for about 1 minute, scraping down the sides of the bowl. Mix in the eggs and yolks, one at a time, scraping down the sides after each. Add the sour cream and vanilla and mix for 30 seconds, until incorporated.
In a medium bowl, combine the flour and salt. Add about 1 cup of the cream cheese mixture to the flour and whisk until smooth. Transfer this mixture back into the bowl of cream cheese and mix until uniformly blended.
Spread the cooled berries evenly over the baked crust. Gently pour the cream cheese batter over the berries, making sure the fruit isn’t pushed to the top.
Bake in the middle of the oven for 20 to 25 minutes. The cheesecake will still be soft, but the top will be a deep brown mahogany color.
Let it cool to room temperature, then refrigerate for at least 2 hours before cutting.
Use the parchment-paper sling to carefully remove the bars from the pan. Use a very thin knife, dipped into hot water, to cut the cheesecake into bars.
