Preheat the oven to 325°f / 165°c. Line 1-2 sheet pans with parchment paper. In a medium bowl, using a handheld electric mixer or a whisk (or you can use a stand mixer fitted with the whisk attachment), combine the Filippo Berio 100% Italian Olive Oil, brown sugar, granulated sugar, and egg. Mix on high speed for about a minute, until the mixture is well combined. Add the vanilla bean paste, salt, cocoa powder, all-purpose flour, rye flour and baking soda and fold in by hand using a rubber spatula.
The dough will seem a little oily and may take a little work to come together - this is ok! Add the chopped chocolate and mix to incorporate. Scoop out ¼ cup balls of dough (about 90g per ball) and roll into rough balls. Press additional chocolate onto the top of each ball if desired (see notes for alternative sizes and baking times)
Bake the cookies for 17-18 minutes, until the edges are set. Remove from the oven and tap the baking sheet briefly on the counter to deflate the cookies slightly. If you would like them perfectly round, use a cookie cutter slightly larger than the cookies to scoot them into a round shape. Finish with flaky sea salt. Allow to cool on the sheet pan for about 20 minutes.
Store leftovers in an airtight container at room temperature.