Preheat your oven to 350°F and grease a standard 12-cup muffin pan with butter or nonstick spray, making sure to coat the bottoms and sides well so the muffins release easily. This gives you time to prepare your ingredients while the oven reaches temperature.
In a medium bowl, whisk together the packed light brown sugar, all-purpose flour, and salt until well combined and any lumps in the brown sugar are broken up. This ensures even distribution of the salt and prevents streaks of unmixed flour in the final batter. Fold in the chopped pecans and chocolate chips, coating them lightly with the dry mixture so they're distributed throughout.
In a separate bowl, whisk together the cooled melted butter, room-temperature eggs, and vanilla extract until the mixture is smooth and well combined. Room-temperature eggs emulsify better with the butter, creating a more cohesive batter, which I've found gives these muffins a better crumb structure.
Pour the wet ingredient mixture from Step 3 into the dry ingredient mixture from Step 2, stirring gently with a spatula until just combined—the batter should look slightly chunky, not overmixed. Divide the batter evenly among the prepared muffin cups, filling each about 2/3 full to allow room for slight rise without overflow.
Bake for 15-17 minutes, until the tops are light golden brown and a toothpick inserted into the center of a muffin comes out with just a few moist crumbs (the chocolate and pecans will create those moist spots—that's the signature fudgy texture of derby pie). Don't overbake, as these muffins are meant to be tender and slightly gooey in the center.
Allow the muffins to cool in the pan for about 5 minutes, which sets them just enough to handle. Run a thin knife or small offset spatula around the edges of each muffin cup to loosen them, then gently pop them out of the pan and transfer to a wire rack. They'll continue to set as they cool, so I like to serve them slightly warm when the chocolate is still soft and the pecans are toasty.