Using a mixer (or using a stand mixer), cream together the 1/2 cup unsalted butter, and 1 1/2 cups light brown sugar, until light.
Add in the 2 large eggs, one at a time, followed by the 1 teaspoon vanilla extract.
Sift or whisk the 2 1/2 cups all-purpose flour, 1/2 teaspoon salt and 1 teaspoon baking soda.
Add alternately to the butter and egg mixture along with the 1 cup sour cream, beginning and ending with the dry ingredients.
Fold in the 2 cups semi sweet or milk chocolate chips. Using a medium-sized cookie scoop, scoop dough onto lined baking sheets.
Bake at 350°F 12-14 minutes, or until edges are lightly golden.
After baking, allow cookies to cool on baking sheets 2-3 minutes, and then move to a wire rack. Frost when completely cooled.
For the browned butter frosting
In a small saucepan, melt 1/4 cup unsalted butter over medium heat; do not stir (swirl pan using handle of the pan only). Continue to cook butter over medium heat until it begins to turn golden brown, swirling gently every so often. Remove from heat once it turns a light amber color (careful to NOT burn). Cool until room temperature.
Add the2 1/2 cups powdered sugar and 1 teaspoon vanilla extract to the cooled browned butter; whisk in the 1 - 2 Tablespoons heavy cream or half and half until it reaches a spreadable consistency.
Frost cooled cookies immediately.
Notes
Browned butter frosting sets quickly; frost cookies immediately after making the frosting
Store cookies in an airtight container for up to 72 hours
Freeze cookies in an airtight container up to 45 days