In a small saucepan over medium-low heat, melt the butter. Continue to cook, stirring frequently, until the little white specks at the bottom of the melted butter turn golden brown. Watch closely because it will go from nicely toasted to burnt very quickly! Remove heat and pour into a heat-safe container and refrigerate until it becomes solid again.
Preheat oven to 325° F. Prepare three 8-inch cake pans by spraying with non-stick spray and lining the bottoms with parchment paper.
In a medium bowl, sift together the baking powder, baking soda, salt, and flour. Set aside.
In the bowl of a stand mixture fitted with a paddle attachment, cream together the brown butter and brown sugar. Add the oil and mix. Add the eggs, one at a time, mixing well after each addition.
With the mixture on low speed, add half of the flour mixture, all of the buttermilk and vanilla extract, then the rest of the flour mixture. Mix until partially combined, then fold in the mini chocolate chips. Be careful not to overmix.
Divide the batter evenly between the pans and bake for 28-33 minutes, or until a toothpick inserted into the middle of the layer comes out clean or with a couple crumbs stuck to it.
Let cool in pans for 10-15 minutes, then turn out onto cooling racks until completely cool. If making ahead of time, wrap with plastic and freeze.