In the bowl of a stand mixer fitted with the paddle attachment, add the butter, light brown sugar, and vanilla extract. Mix on low until combined, then continue to cream butter and sugar for 5 minutes until light and fluffy.
Add the eggs, all purpose flour, rye flour, baking powder, baking soda, and sea salt in that order and mix on low until combined into a dough. Add the chocolate chips, and mix on low to combine.
Line a baking sheet with parchment paper. Using your hands, form the dough into 18 balls and place them on the prepared baking sheet. Place the baking sheet in the fridge for 1 hour.
Preheat the oven to 375°F. Line another baking sheet with parchment paper. Transfer half the cookies to the second baking sheet, and space them 1-inch apart.
Bake for 12 to 15 minutes or until lightly browned on the bottoms. Sprinkle with flaky sea salt immediately after they come out of the oven. Allow to cool completely on the baking sheet.
Store in an airtight container for up to 7 days.