Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a medium bowl, whisk together the all-purpose flour and baking soda. Set aside.
In a large bowl, using an electric mixer, beat 1 cup softened butter, granulated sugar, light brown sugar, and salt on medium speed until creamy, about 2 minutes.
Add the vanilla extract and eggs, one at a time, beating well after each addition.
Gradually add the flour mixture to the butter mixture, beating on low speed until combined.
Stir in the semisweet chocolate chips with a spatula.
Drop rounded tablespoons of dough about 2 inches apart onto the prepared baking sheets.
Bake for 10 to 12 minutes or until the edges are golden but the centers are still soft.
Remove from oven and let cookies cool on baking sheets for 5 minutes, then transfer to wire racks to cool completely.
To prepare the frosting, in a medium bowl, beat 1/2 cup softened butter until smooth and creamy.
Gradually add powdered sugar, beating until combined.
Add vanilla extract and heavy cream, and beat on high speed until light and fluffy, about 2 minutes.
Once cookies are completely cool, spread about 1 tablespoon of frosting onto the flat side of one cookie.
Top with another cookie, flat side down, to form a sandwich.
Repeat with remaining cookies and frosting.
Serve immediately or refrigerate in an airtight container for up to 3 days.