Preheat the oven to 350 F and line two baking sheets with parchment paper.
Stir the flour, brown sugar, cinnamon, and melted butter together until small clumps form. Refrigerate the crumble while preparing the cookie dough.
Beat the softened butter, granulated sugar, and brown sugar until light and creamy. Mix in the egg, vanilla, and lemon zest.
Whisk the flour, baking powder, baking soda, and salt in a separate bowl. Add the dry ingredients to the butter mixture and mix just until combined.
Divide the dough into 12 portions and arrange them on the prepared baking sheets. Press a deep indentation into each portion and fill each one with about 1 1/2 teaspoons of blueberry preserves.
Scatter the chilled crumble over the cookies, gently pressing it around the preserves. Bake for 12 to 14 minutes, until the edges are lightly golden.
Cool the cookies on the baking sheets for 10 minutes, then transfer them to a cooling rack and let the blueberry centers finish setting.