Line an 8-inch square pan with parchment paper, leaving overhang on two sides for lifting.
In a medium heavy saucepan, combine the granulated sugar, whole milk, and unsalted butter. Set over medium heat and stir until the sugar dissolves and the mixture comes to a gentle boil, 3–5 minutes.
Continue boiling, stirring frequently, until the mixture reaches 236–240°F (soft-ball stage) on a candy thermometer, 4–6 minutes more. If you don’t have a thermometer, a small spoonful dropped into cold water should form a soft, malleable ball.
Remove the pan from the heat. Immediately add the marshmallow creme, creamy peanut butter, vanilla extract, and fine sea salt. Stir steadily until fully melted and smooth, 1–2 minutes.
Scrape the fudge into the prepared pan and smooth the top with a spatula.
Let cool at room temperature until set, 2–3 hours, until the surface is firm to the touch and a knife cuts cleanly. Lift out using the parchment overhang and cut into 36 squares. Store airtight at cool room temperature for up to 1 week.