First, candy the walnuts. Melt 2 tablespoons of the butter in a medium pan over medium heat. Add the brown sugar and cook until the sugar softens and darkens slightly, about 2 minutes. Add the walnuts and stir to coat them in the brown sugar and butter mixture. Toast them in the pan until lightly golden on all sides, staring every minute, for about 5 minutes. Remove from heat, empty the walnuts onto a flat baking sheet lined with parchment paper, and allow to cool.

To prepare the grilled cheese, cut a bijou in half and place two halves side by side on a piece of bread. Drizzle 1 tablespoon of honey over the bijou and sprinkle the walnuts over it. Place a piece of bread over the filling and press down to compress it slightly. Repeat to assemble the second sandwich.

Melt the remaining 2 tablespoons of butter in a cast iron skillet over medium high heat. Add the sandwiches and cook until the bread is golden and toasty on both sides and the cheese is melted, about 4 minutes per side. Serve immediately.