1. In a large mixing bowl, beat together butter and sugars until no lumps remain, 1-2 minutes. Beat in eggs and vanilla extract, scraping the sides of the bowl to make sure all of the ingredients are incorporated. Add flour, baking soda, salt, and mix until smooth. Stir in mini chocolate chips. Cover and refrigerate dough for at least 1 hour or overnight.
2. Preheat oven to 350 degrees F. Roll chilled dough into smooth, tablespoon-size balls, about 1 inch in diameter. Flatten balls slightly into 3/4-inch disks. Place disks about 2 inches apart on parchment or Silpat lined baking sheets. Bake for 9-11 minutes, or until cookie edges are slightly golden brown. Let cookies cool on baking sheet for about 5 minutes. Transfer to a wire rack and cool completely.
3. To prepare the cookie dough filling, beat together butter and brown sugar in a large bowl with an electric mixer on medium speed until light and fluffy, about 2-3 minutes. Mix in flour, powdered sugar, and salt on low speed until incorporated. Slowly add heavy cream and vanilla extract and beat until fluffy, about 2 minutes. Stir in mini chocolate chips.
4. To assemble, sandwich 1 heaping tablespoon of filling between two cookies. Press cookies lightly until filling spreads to the edges. Repeat with remaining cookies.
Note: Sandwiches can be stored refrigerated in an airtight container, for up to 3 days. Let them sit at room temperature for 30 minutes before serving.