Prepare the Cake: Preheat oven to 350°F. Combine chocolate chips and butter in a medium-size microwavable glass bowl. Microwave on HIGH until melted and smooth, about 2 minutes, stirring every 30 seconds. Cool 10 minutes.
Beat eggs, granulated sugar, and light brown sugar in the bowl of a heavy-duty stand mixer fitted with whisk attachment on medium speed until thick and creamy, about 5 minutes. Whisk together flour, cocoa, baking powder, and salt. Add flour mixture and melted chocolate mixture to egg mixture in batches, beginning and ending with flour mixture. Beat on low speed just until each is incorporated. Pour batter into a 12-inch cast-iron skillet.
Bake in preheated oven until a wooden pick inserted in center comes out with a few moist crumbs, about 40 minutes. Place on a wire rack to cool slightly.
Prepare the Frosting: Combine granulated sugar, butter, milk, cocoa, flour, and salt in a small saucepan over medium. Cook, stirring constantly, until mixture comes to a boil, about 5 minutes. Cook, stirring constantly, until slightly thickened, about 1 minute (it will still be a bit thin). Remove pan from heat, and stir in vanilla extract. Pour into a medium-size heatproof bowl, and let cool slightly, about 15 minutes. Pour warm Frosting over warm Cake. Sprinkle with chopped pecans. Serve warm or at room temperature with ice cream.