Preheat oven to 325° F. Line two cookie sheets with parchment paper or silicone baking mats.
Whisk the flour, baking soda and salt together in a medium bowl. Set the bowl aside.
Whisk the olive oil and brown sugar together until thoroughly combined. Add the egg, yolk, and vanilla to the bowl and mix with a hand-held mixer until combined. Add 1/2 of the dry ingredients to the bowl of wet ingredients and beat until combined and then add the other half until combined.
Stir in the dairy-free chocolate chips. The dough will be thick and a little dry but that is normal. Also the chocolate chips may not all mix into the batter, but that's ok. Try to mix them in as best that you can then save them to put on top of the cookies later.
Scoop golf ball sized balls of dough and roll the dough into balls in your hands and then put them onto the cookie sheets. Push in some of the spare chocolate chips into the tops of the cookies.
Bake for 12-14 minutes. Do not over-bake. The cookies won't be golden, but the tops will have puffed up. Basically the cookies will look puffy and soft but if you touch the tops, they will be set.
Cool cookies on cookie sheets for a few minutes, then let them continue cooling on wire racks or plates.