In a large saucepan over medium heat, melt the butter, corn syrup, and brown sugar together. Stir frequently until the mixture comes to a gentle boil. Allow it to boil for 1 minute without stirring, then remove from heat.
Stir in the vanilla extract and salt until well combined.
In a large mixing bowl, combine the Golden Grahams cereal and mini marshmallows. Pour the melted butter mixture over the cereal and marshmallows, stirring until everything is evenly coated.
Gently fold in the chocolate chips until just combined.
Line a 9x13-inch baking dish with parchment paper, leaving some overhang for easy removal. Pour the mixture into the prepared dish and press it down firmly with a spatula or your hands to create an even layer.
Allow the bars to cool at room temperature for about 30 minutes, or until set. For quicker cooling, you can refrigerate them for about 15 minutes.
Once set, lift the bars out of the dish using the parchment paper and cut into squares.