Preheat the oven to 350ºF. Line an 8-inch square pan with non-stick parchment paper.
Brown the butter: In a large stainless steel pan or deep skillet placed over medium heat, add the butter. The butter will melt, then sizzle and foam. When the butter starts to foam, use a rubber spatula to continuously stir so that it doesn’t burn. As the foam subsides, you’ll see and smell that the butter has browned. It will have a nutty aroma when ready. This process will take between 8-15 minutes, depending on your pan and stove heat. Once browned, transfer the butter (including the dark flecks) to a large mixing bowl and let it cool for 10 minutes.
To the cooled butter, add the brown sugar. Beat on medium-high speed for 1 minute. The mixture will still look very grainy at this stage, which is fine.
Add the eggs and vanilla, and beat on medium-high speed for 1 minute. The mixture will become pale and silky smooth.
Sift the flour and salt into the mixing bowl, then gently fold together with a rubber spatula. Do not overmix.
Add ¾ of the chopped chocolate and gently fold through.
Transfer the blondie batter into the prepared pan. The batter will be thick but still silky. Use the back of a spoon or an offset spatula to smooth it into an even layer.
Top with the remaining chopped chocolate.
Bake in the middle of the preheated oven for 25 minutes. The edges of the blondie will look firm, but the center may still appear soft—it will firm up as it cools.
Remove from the oven and let cool completely in the pan before turning out and cutting into slices or squares. Sprinkle with a little sea salt before serving.