Position a rack in the upper third of the oven. Preheat the oven to 350°F (180°C). Line an 8-inch (20-centimeter) square baking pan with parchment paper or aluminum foil, leaving an overhang around each side.
In a medium saucepan, melt the butter over low heat. Remove the saucepan from the heat and with a wooden spoon or sturdy silicone spatula, mix in the brown sugar, vanilla, and salt until relatively smooth. Quickly stir in the egg and mix until smooth and lump-free. Add the flour, chocolate chips, and walnuts (if using) all at once. Stir the mixture until just incorporated. Spread the batter evenly in the prepared pan.
Bake for 23 to 30 minutes, until the blondies are golden and crinkly on top, set in the middle, and a toothpick or cake tester plunged into the center comes out clean or with just a few stray crumbs attached.
Let the blondies cool completely in the pan. (Hah! We know the temptation. Trust us, we know. Still, try to wait. These blondies are better after they rest a little.) Lift the ends of the parchment paper and transfer the entire block of blondies to a cutting board. Cut the block into rows of 4, 5, or 6 to yield 16, 25, or 36 squares. The blondies will keep in an airtight container at room temperature for up to 5 days. (Hah! As if you'll be able to resist for that long.)