Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, salt and baking soda, then set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter with the brown sugar and granulated sugar on medium speed until light and fluffy, 3 to 5 minutes. Add 2 teaspoons of the vanilla extract and the eggs and blend until incorporated. Lower the speed to a stir, add the flour and mix until just combined. Then stir in 2 cups of the chocolate chips until incorporated.
Drop the dough in teaspoon-size balls 2-inches apart onto the prepared baking sheets. Bake until the cookies are golden and crisp, 12 to 15 minutes. Cool the cookies for 5 minutes in the pan and then transfer to a wire rack to cool completely.
Whip the heavy cream, confectioners' sugar and the remaining 1 tablespoon vanilla until medium peaks form. Place about 1/4 cup of the whipped cream in a 9-inch circle on a cake plate and then cover the whipped cream with some cookies. Layer 1 cup whipped cream over the cookies and arrange another layer of cookies over the top. Repeat the layers three more times, finishing with a layer of cream. Sprinkle the remaining 1/2 cup chocolate chips over the top. Refrigerate the cake until the cookies soften, at least 4 hours or up to overnight.
Slice into wedges to serve.