Preheat the oven to 350F/175C and line a baking sheet with parchment paper.
Melt the butter in a small sauce pan. Once there are only a few small lumps of butter left, take it off the heat and keep on stirring until all the lumps are melted. Now pour the butter in a bowl and set it aside to cool off.
Sift flour, baking soda and baking powder and add salt to it. Mix it all together and set it aside.
Add the cane sugar and brown sugar to the slightly cooled off melted butter and beat it with a whisk until fully combined. Then add the egg, egg yolk, lemon zest and juice and beat it until it turns a pale color.
Add the dry ingredient mixture to the wet with a wooden spatula. Combine until everything is just incorporated. A few streaks of flour is not a problem at all. The cookie dough should be pretty firm. If it is runny, add a bit more flour, starting with a tablespoon.
Add the frozen blueberries to the cookie dough and fold them in with the same wooden spatula. The blueberries will bleed a little bit, but that is ok. Prevent it from turning completely purple (grey) by not over mixing the dough.
With a large cookie scoop, scoop dough on a lined baking tray, leaving enough space between the cookies so they have some room to spread. The dough should be enough for 8 large cookies. Optionally, once the cookies are scooped out, press in a few extra blueberries. This is pure for aesthetics.
Bake the cookies for 10-12 minutes until the edges are firm and slightly browned. Then take them out of the oven and let them cool off for 5-10 minutes. To completely cool them off, transfer them to a cooling rack for another 10 minutes.