Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. In a large mixing bowl, combine softened salted butter, light brown sugar, and granulated sugar. Whisk until creamy and smooth, about 2-3 minutes. Add the egg and vanilla extract, beating until fluffy and well combined.

In another bowl, whisk together all-purpose flour, baking powder, and baking soda. Gradually incorporate the dry ingredients into the creamed butter mixture, mixing until just combined.

Using a cookie scoop, portion the dough onto the prepared baking sheet, leaving space between each cookie. Flatten gently into a disc shape and bake for approximately 12 minutes, or until the edges are lightly golden.

While the cookies bake, prepare the berry filling. In a medium pot, combine the frozen mixed berries and granulated sugar over medium-high heat. Cook for about 5 minutes until bubbly. Remove from heat, add lemon juice, and cool slightly.

In a separate bowl, mix melted butter, all-purpose flour, and granulated sugar until crumbly. Ensure it's clumpy enough to hold together.

Once the cookies are out of the oven, create an indentation in the center of each cookie. Spoon the berry filling into each cookie and sprinkle the crumb topping over the filling. Allow to cool for 15 minutes before serving.