Grease an 8x8 inch baking pan and line with parchment paper, leaving an overhang on the sides.
In a large saucepan, combine butter, granulated sugar, brown sugar, evaporated milk, and corn syrup. Cook over medium heat, stirring constantly, until sugar is dissolved.
Bring the mixture to a boil, then reduce heat to low and simmer for 5 minutes, stirring occasionally.
Remove from heat. Stir in vanilla extract, chocolate chips, and marshmallows until melted and smooth.
Pour the mixture into the prepared baking pan and spread evenly. If desired, sprinkle with flaky sea salt.
Let the fudge cool completely at room temperature, or chill in the refrigerator for about 2 hours until firm.
Once firm, lift the fudge out of the pan using the parchment paper. Cut into 16 squares.
Notes
Store fudge in an airtight container at room temperature for up to 2 weeks.