Step 1: Prepare the crust. Preheat oven to 350°F (175°C). In a medium bowl, combine graham cracker crumbs, ¼ cup granulated sugar, and melted butter. Press mixture firmly into the bottom of a 9-inch springform pan. Bake for 10 minutes, then set aside to cool.
Step 2: Make the filling. Reduce oven temperature to 325°F (160°C). In a large bowl, beat softened cream cheese and 1 cup granulated sugar with an electric mixer until smooth and creamy.
Step 3: Add eggs and vanilla. Beat in the eggs one at a time, mixing just until combined after each addition. Stir in the vanilla extract and sour cream until smooth. Gently fold in the ½ cup of mini marshmallows.
Step 4: Bake the cheesecake. Pour the filling over the cooled crust in the springform pan. Place the springform pan on a baking sheet to catch any drips (or in a water bath). Bake for 60-70 minutes, or until the edges are set and the center jiggles slightly when gently shaken.
Step 5: Cool and chill. Turn off the oven, crack the door open, and let the cheesecake cool inside for 1 hour. Remove from oven and let cool completely on a wire rack. Once cool, cover and refrigerate for at least 4 hours, or preferably overnight, until thoroughly chilled.
Step 6: Add marshmallow topping. Just before serving, arrange the remaining 3 cups of mini marshmallows evenly over the top of the chilled cheesecake.
Step 7: Toast the marshmallows. Use a kitchen torch to toast the marshmallows until golden brown and slightly charred. Alternatively, place under a broiler for 1-2 minutes, watching carefully to prevent burning. Serve immediately and enjoy!