Melt butter in a saucepan over medium heat, stirring often, until it turns golden brown and smells nutty. Cool until room temperature.
Preheat oven to 350°.
In a large mixing bowl, add brown butter, vegetable oil, granulated sugar, and powdered sugar, beat with a mixer until smooth. Beat in the eggs and vanilla.
Add flour, baking soda, cream of tartar and kosher salt. Mix on low speed until combined, raise to medium speed and beat about 2 minutes.
Use a 1 inch cookie scoop to form cookie balls. Place reserved 1/2 cup sugar in a shallow bowl. Roll cookie balls in sugar and place about 2 inches apart on a lined baking sheet.
Smash cookie balls with a cookie stamp or bottom of a glass.
Bake cookies for 10-12 minutes until lightly browned on the bottoms.
Cool on baking sheet for a few minutes and then move to a wire rack to cool.
Melt chocolate chips with heavy whipping cream in a small pan over low heat, stirring until smooth (or microwave in 15 second intervals, stirring in between).
Spread chocolate onto half of each cookie and sprinkle with chopped pistachios. Place in a single layer of a cookie sheet or wire rack until set up or refrigerate for about 15 minutes to set up faster.