First things first, make sure you have your butter softened or at least softening. You do not want cold butter for cookies. Your butter should be very soft and easily mixable.
In a sauce pan over medium heat, add the blueberries, sugar, and lemon juice. Stir to combine and let the blueberries start breaking down. Mash some of them but leave some whole (they'll burst, but you want chunks). Let the liquid reduce for about 5 minutes on low/medium heat and then transfer to a Tupperware and put in the fridge to cool.
In a large bowl, add the flour, baking powder, and salt. Whisk together to combine and set aside.
In another large bowl, using a hand or stand mixer, cream together the softened butter and sugar for about 45 seconds until mixed and creamy. Add in the egg and vanilla, mix again. Pour in your dry ingredients and mix just until combined, make sure to not overmix.
Chop up one of your chocolate bars into chunks and pour into dough. Mix well. Add in your blueberry compote in dollops throughout. Using a knife, swirl the blueberries into the dough. This gives your cookies a really pretty blueberry swirl color. If you used a spoon to stir, the entirety of the dough would turn blue, which would still make for gorgeous cookies but the swirl is ideal.
Cover and set the dough in the fridge for at least 35 minutes but ideally 1 hour. You want the dough cold before baking.
Preheat your oven to 375 and place golf ball sized dough on a cookie sheet, add a few more chocolate chunks on each cookie from the second chocolate bar.
Bake for 15-18 minutes. This will vary on oven, baking sheet being used, and preferred texture of your cookie! So just keep an eye on them and remove from the oven when the edges are slightly golden brown.
Remove from oven and let rest for 5 minutes before transferring to a wire rack to cool.
This should make 12-14 cookies, enjoy!