Preheat the oven to 325°F. Line an 8-inch square baking pan with parchment and set aside.
Combine the butter and 1 cup chocolate chips in a medium-sized saucepan over medium-low heat. Stir as it melts and then stir until smooth. Remove from the heat.
Add the sugar and vanilla and stir to combine. Whisk in the eggs, one at a time, stirring until smooth and shiny between each egg. Add the flour and salt. Stir until just incorporated.
Stir in the walnuts and additional ½ cup chocolate chips. Pour the batter into the parchment-lined pan; bake until a toothpick or cake tester inserted in the center comes out with wet crumbs, about 45 minutes. (See note below.)
Cool the brownies in the pan on a wire rack before slicing.
Notes
If you wait until a toothpick inserted comes out clean, they will be overcooked. You want fudge-like crumbs.