Position an oven rack in the center of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment paper and draw a 6-inch circle in the center of each. Dust the parchment with flour.
Whisk together the flour, baking soda and salt in a large bowl.
In a second large bowl, beat together the butter, brown sugar and granulated sugar with an electric mixer on medium-high speed until light and fluffy, about 4 minutes. Add the eggs, one at a time, beating to incorporate after each addition. Beat in the vanilla. Reduce the mixer speed to low and add the flour mixture, beating just until incorporated. Stir in the chocolate chips.
Divide the dough into eight portions. Transfer one portion to the center of the circle on one of the prepared baking sheets. Press flat, then dust with more flour and place another sheet of parchment paper on top. With a rolling pin, roll the dough out into a 6-inch circle, using the circle on the parchment as your guide. Remove the top piece of parchment and bake until almost done, about 12 minutes. Immediately transfer the cookie with its parchment to a work surface. Lay a piece of parchment on top of the cookie and flip the cookie and parchment over. Using a rolling pin, gently roll to compress the cookie. Then use the parchment to roll the cookie around a large waffle cone filled and wrapped in foil. Let the cookie cool completely before removing the cone, about 15 minutes.
Repeat with the remaining cookie dough and the other baking sheet, timing batches to finish baking right when it's time to remove the cone from the cooled cookie.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)