Preheat oven to 350 degrees F. Line two baking sheets with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment or in a large mixing bowl using a hand mixer, beat the softened butter, brown sugar, and granulated sugar until creamy.
Add the egg and vanilla extract. Beat to combine.
On low speed, mix in the flour, baking soda, and salt until there are no dry spots. Add the chocolate and mix until it is evenly distributed throughout the cookie dough.
Divide the cookie dough into 7 equal sections, about 3.5 ounces each. Roll the cookie dough into balls, then gently press each ball into a disk shape about 1/2 an inch thick and place onto the parchment lined baking sheets. (Place 2 cookies at a time on each baking sheet.) The cookies will spread as they bake, so make sure that there is enough distance between the two cookies.
Bake the cookies for 10-12 minutes. Allow the cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely. Repeat until all 7 cookies are baked.
To make the ganache, place the chocolate in a heat-proof mixing bowl. Heat the cream, being careful not to let it boil over. Pour the hot cream over the chocolate and let it stand for a few minutes. Mix until all of the chocolate is melted and the mixture is smooth. Allow to cool completely until it is a spreadable consistency. If you are in a hurry, you can stick your ganache in the refrigerator for about 20 minutes, or until it is firm enough to spread.
Assemble cookie cake: To assemble, spread 3 tablespoons of the chocolate ganache over the first cookie layer. Using a small offset spatula, spread the ganache evenly over the cookie reaching almost to the edges. Press the second cookie layer on top and repeat until you have used up all of the cookies. End with a cookie layer.
Carefully, wrap the cake with plastic wrap and place it in the refrigerator for at least 30 minutes. Once the ganache has fully set, remove the plastic wrap from the cake and serve at room temperature.