To the bowl of a stand mixer fitted with the paddle attachment, add the eggs and beat on medium-high speed until foamy.
Add the flour, sugars, vanilla, salt, and beat on medium speed to incorporate. Stop to scrape down the sides of the bowl as necessary.
Add the butter and beat on medium-high speed until creamy and incorporated, about 1 to 2 minutes. Stop to scrape down the sides of the bowl as necessary.
In the bottom of the pie shell add the chocolate. Pour the cookie batter on top, smoothing the top lightly with a spatula.
Place pie on a baking sheet (insurance against overflow) and bake for about 50 to 52 minutes, or until a toothpick or knife inserted halfway between the center and the edge comes out clean. I baked for 50 minutes and the center was gooey like the center of an underbaked chocolate chip cookie. If you prefer less gooeyness, bake 5 to 10 minutes longer. All ovens, climates, ingredients, etc. vary so use your judgment about how long to bake.
Place pie on wire rack to cool for at least 2 hours before slicing and serving. Don't slice early or you will have a gooey mess.
Optionally before serving, evenly drizzle with hot fudge. Alternatively, serve with ice cream or whipped topping. Pie will keep airtight at room temp for up to 5 days.