Place the butter in a 10-inch cast iron skillet. Cook over medium heat until the butter melts and begins to foam.
Continue cooking, stirring occasionally, until brown specks begin to form at the bottom of the pan and the butter has a nutty aroma.
Remove the pan from the heat. Add the brown sugar, and stir until combined. Allow to cool slightly.
Preheat oven to 350°F (175°C).
Add the eggs and vanilla to the cooled butter mixture, and stir until combined.
Add the flour, baking power, and salt, and mix just until combined. (Add the flour in portions and stir gently to prevent a mess.)
Stir in the chocolate chips and nuts. Spread the batter evenly in the pan. If desired, sprinkle the top with a pinch or two of coarse salt.
Bake 25 to 30 minutes, or until the blondie is golden brown and a pick inserted into the center comes out clean. (Be sure not to over-bake.)
Serve warm with ice cream and caramel or chocolate sauce, if desired.
Notes
If you prefer, you can transfer the brown butter to a mixing bowl and mix the batter in that bowl. Then just transfer the mixed batter to the skillet and bake.