Position a rack in the center of the oven and preheat to 350 degrees F. Melt the butter in a 10-inch cast-iron skillet over medium heat, then set aside to cool slightly, 5 minutes.
Whisk the granulated sugar, brown sugar, eggs, and vanilla together in a large bowl until smooth. Stir in the melted butter. (Do not wipe out the skillet.) Whisk the flour, cocoa powder, salt and baking soda together in another bowl. Stir the dry ingredients into the wet ingredients, mixing well with a wooden spoon until dough is homogenous (do not overmix). Stir in the chocolate chips.
Use a rubber spatula to scrape the dough into the prepared skillet, gently spreading it to the edges and smoothing the top. Bake until the top is cracked, the edges are brown and crisp and the center is still soft, 40 to 45 minutes. Cool on a wire rack for 15 minutes. Serve warm, cut into wedges.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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