Line a 9-inch square baking pan with parchment paper.
Combine chocolate chips, sweetened condensed milk, and vanilla extract in a heavy saucepan over medium-low heat; stir until melted, about 5 minutes. Pour into the lined baking pan.
Bring sugar, milk, and butter to a boil in another saucepan over medium heat. Cook at a boil until mixture turns golden and thickens slightly, 5 to 7 minutes. Pour in cream carefully; it may hiss and splatter. Bring back to a boil. Remove from heat; stir in butterscotch chips and marshmallow cream until smooth.
Pour butterscotch layer over the chocolate layer in the pan; sprinkle with sea salt. Allow fudge to cool to room temperature, about 30 minutes. Refrigerate until firm, about 2 hours.