Preheat oven to 350°F and line two baking sheets with parchment paper, then whisk together flour, baking soda, and salt in a bowl.
In a large bowl, whisk together olive oil and both sugars until well combined, then add eggs and vanilla, whisking until smooth and emulsified.
Stir the flour mixture into the wet ingredients until just combined, then fold in chocolate chips and toasted walnuts.
Scoop rounded tablespoons of dough onto prepared baking sheets, sprinkle with flaky sea salt, and bake for 10-12 minutes until edges are set but centers are still soft.
Allow cookies to cool on the baking sheet for 3 minutes before transferring to a wire rack to finish cooling.