In a large saucepan, melt the butter over medium heat. Once melted, stir in the brown sugar, corn syrup, and salt. Bring the mixture to a gentle boil, stirring constantly for about 2 minutes until it thickens slightly. Remove from heat and stir in the vanilla extract.

In a large mixing bowl, combine the Golden Grahams cereal and mini marshmallows. Pour the warm butter mixture over the cereal and marshmallows, and stir until everything is evenly coated.

Line a 9x13-inch baking dish with parchment paper, leaving some overhang for easy removal. Pour the cereal mixture into the prepared dish and press it down firmly with a spatula or your hands to create an even layer.

Sprinkle the chocolate chips evenly over the top of the pressed mixture. Allow the bars to cool at room temperature for about 30 minutes, or until set.

Once cooled, lift the bars out of the baking dish using the parchment paper. Cut into squares and serve.