Butter a 9x13 glass baking dish. Set aside.
Melt butter in a large saucepan over low heat.
Add evaporated milk and sugar and stir frequently, allowing the sugar to fully dissolve (~5 minutes).
Once the sugar has fully dissolved, increase the temperature to medium and allow the fudge to reach a rolling boil. Stir constantly for 4 minutes.
Remove from heat and add chocolate chips and marshmallows. Stir until completely combined and smooth (~2 minutes).
Add vanilla extract. Stir until completely smooth (~1 minute).
Pour into the buttered dish and smooth to distribute evenly around the pan.
Allow it to set (~45 minutes) before cutting. Store in an air-tight container at room temperature.
