Caramelise the onions: Melt 2 tablespoons of butter with 2 tablespoons of olive oil in a large saucepan over medium-high heat. Add the thinly sliced onions, bay leaves, and a pinch of salt. Cook for 1 hour, stirring often.
Add thyme: During the last 15 minutes of cooking, add the chopped thyme to the onions and stir well.
Grill the Wagyu burgers: Season the Wagyu burgers with salt on both sides. Grill them using the 3-4-1 method: 3 minutes on one side, 4 minutes on the other, and then 1 minute on the last side. During the last minute of grilling, add about 50g of blue cheese to each burger to melt.
Toast the buns: Butter the inside of the burger buns with softened butter and toast them.
Assemble the burgers: Start with the toasted bun, add some caramelised onions, place the Wagyu burger patty with melted blue cheese on top, add a handful of rocket, and then cap it with the other half of the toasted bun. Enjoy!