Place a saucepan filled with one inch of water over medium heat and bring to a simmer. Set a heatproof bowl over the simmering water, taking care that the bottom of the bowl is not touching the water, and melt the chocolate and butter together, stirring occasionally. Once melted, remove from the heat and let the mixture cool slightly.

In a small bowl, whisk together the rye flour, baking powder, and salt.

Place the eggs in the bowl of a stand mixer fitted with a whisk attachment. Whip on medium-high, adding the sugar a few tablespoons at a time, until all the sugar is incorporated. Turn the mixer to high and whip until the eggs have tripled in volume and turned very light yellow and fluffy, about 6 minutes.

Reduce the mixer to low and add the melted chocolate mixture followed by the vanilla. Mix to combine, scraping down the sides of the bowl as needed, then add in the flour mixture and stir until just combined. The dough will be very soft.

Refrigerate dough until it just firm to the touch, about 30 minutes. If cooled too long, the dough will be hard to scoop.

Preheat oven to 350º . Line two baking sheets with parchment paper or silicone mats. Remove the dough from the fridge and scoop with a rounded tablespoon onto the baking sheets, shaping the balls of dough into rounds and spacing them 2 inches apart. Top each mound of dough with a few flakes of sea salt, pressing gently so it adheres.

Bake for 8 to 10 minutes, until the cookies have puffed up and have a smooth bottom and rounded top with a few small cracks. Remove the baking sheets from the oven and cool slightly then transfer to a wire rack and let cool completely. The cookies with keep up to 3 days in an airtight container.