Preheat the oven to 325F.
In a large bowl, beat the butter and sugars for a couple minutes, until pale and fluffy. Beat in the eggs and vanilla. Add the flour, baking soda and salt and stir or beat on low speed until almost combined; add the chocolate chips and stir just until the dough comes together.
Scoop about 1/3-1/2 cup of dough onto a parchment-lined baking sheet; you should be able to fit two on one larger sheet, spacing them well apart. Cover with a piece of waxed or parchment paper and press down to flatten them to about 1/2" thick. Peel off the paper.
Bake for about 14 minutes, until pale golden and just set. Transfer to a wire rack to cool completely.
Spread cooled cookies generously with frosting, stacking them as you go. Let sit for several hours, then slice into thin wedges, or remove each cookie from the stack to serve.