Preheat oven to 350°F. Line 3 (8-inch) cake pans with parchment and spray with baking spray. Set aside.
Cream butter and sugar until light and fluffy, about 5 minutes.
Meanwhile, reserve 2 tablespoons of flour in a small bowl. In a medium bowl, whisk the remaining flour with the salt and baking powder.
Add the eggs to the butter and sugar mixture, one at a time, scraping the bowl as needed. Add the vanilla.
Add a third of the flour mixture to the wet mixture, then add half the milk. Continue adding the flour and milk, ending with the flour, and beat each addition until just incorporated, being careful to not overmix.
Toss the mini chocolate chips in the reserved flour, then fold into the batter by hand, scraping the bottom and sides of the bowl.
Divide the batter evenly among the three cake pans. Bake in the preheated oven until a toothpick comes out clean, about 20 minutes. Let cool in pans for 15 minutes, then turn out and cool completely on a wire rack, approximately 1 hour.