Preheat the oven to 350°F with a rack in the center.
Spray an 8-inch x 8-inch baking pan with cooking spray and line it with a piece of parchment paper to cover the bottom and come up two opposite sides.
In the microwave or a double boiler, combine the butter and white chocolate. Heat, stirring occasionally, until just melted and smooth. If melting in the microwave, use half power in 30-second bursts, stopping to stir thoroughly in between.
In a large bowl or the bowl of a stand mixer fitted with the paddle, beat the eggs until frothy, about two minutes.
Add the brown sugar and the vanilla and beat to combine thoroughly.
Pour in the butter-white chocolate mixture and beat until well combined.
Add the flour and salt, and mix with a spatula until just combined.
Add the chocolate chips and walnuts and stir to distribute.
Scrape the batter into the prepared pan.
Bake for about 30 minutes, until browned around the edges and just the tiniest bit jiggly in the very center — the blondies will firm up as they cool.
Cool for at least 30 minutes, then run a knife around the edges.
If cutting into squares while still warm, cut in the pan. If cooled, you can use the parchment paper "handles" to remove the whole batch from the pan before cutting.
Cut into squares and serve.