How to Make It
Beat together olive oil and sugars in the bowl of a heavy-duty stand mixer fitted with paddle attachment on medium speed until fully incorporated, about 1 minute. Add eggs and vanilla, and beat just until combined, about 30 seconds (do not overbeat).
Whisk together flour, baking soda, baking powder, and salt in a large bowl until fully combined and no clumps. Add flour mixture to olive oil mixture, and beat until fully combined, about 1 minute. Scrape down sides of bowl as needed. Remove paddle attachment, and fold in chocolate chunks with a rubber spatula. Cover and chill dough until firm and cooled through, about an hour.
Meanwhile, preheat oven to 400°F. Line 2 baking pans with parchment paper. Remove dough from refrigerator just before using. Scoop out 1 1/2-inch size balls, and place on lined baking sheet spaced about 2 inches apart (about 9 cookies per baking pan). Bake in preheated oven until edges are beginning to turn golden, about 8 minutes. Let cool on a wire rack for 15 minutes. Repeat with remaining dough. Sprinkle cookies with sea salt.