Preheat the oven to 250ºF. Position the oven racks to the upper third and lower third positions. Line 2 large baking sheets with parchment paper. Set them aside.
Start melting the butter in a saucepan over medium heat. Keep heating the butter after it has melted. You'll notice that the melted butter froths up, which is a bit distracting because you can't tell if the butter is browning at this phase. Just give everything a stir. After a while, the butter will bubble feverishly and create a pleasant popping sound for about a minute. Wait a little longer and the butter will start to turn a golden color. Stir the butter frequently to keep it from burning. Then, the butter bits on the bottom will start to turn brown, like the color of coffee grounds. You want to turn off the heat right before the bits turn black, an indication that you've left the butter in there for too long. This entire process should take about 4 to 5 minutes after the butter has melted. Turn off the heat.
Mix the maple syrup, soy sauce, vanilla and salt into the browned butter. Whisk to combine.
Take out 2 large bowls. Divide the corn chex, pretzels and nuts between the 2 bowls. Mix up the contents in each bowl. Divide the syrup mixture between the two bowls. Stir to coat the dry ingredients with the syrup. Sprinkle 1/4 cup of furikake in each bowl. Stir again to distribute the furikake.
Spread the furikake chex mix over the baking sheets. Bake for 1 hour, stirring halfway through baking. Enjoy the sweet smell of butter and sugar wafting around your house as the chex mix bakes.
Remove the chex mix from the oven. Give everything another stir. You can sprinkle more furikake over the chex mix, if you like. The chex mix will turn crunchy as it cools.
Store the chex mix in an airtight container. It will keep for 1 to 2 weeks, if it lasts that long.