In a saucepan over low heat, melt the butter, stirring gently until fully liquid. Remove from heat, add the white chocolate chips, and let sit for about 5 minutes. Whisk until smooth and let cool at room temperature for around 30 minutes.

In a large bowl, combine the cooled mixture with granulated sugar, whisk well, then add vanilla extract and eggs one at a time, whisking until fully combined.

Sift in flour and salt into the wet ingredients, folding in with a spatula until just combined. Gently fold in fresh blueberries.

Preheat the oven to 350°F (175°C). Prepare an 8x8-inch baking dish by greasing it or lining it with parchment paper. Pour the batter into the dish and bake for 35-45 minutes, until golden.

Allow to cool for about 10 minutes in the baking dish, then transfer to a wire rack to cool completely. Slice into 12-16 pieces.