Mix enough cold milk with the sweetened condensed milk to equal 3 cups. Mix in vanilla. Gradually add pudding mix, stirring continually for 2 minutes; put in refrigerator.
Melt butter in saucepan and add crushed graham crackers. Stir over medium heat until lightly browned. Remove from heat.
Beat 1 cup of heavy whipping cream until peaks form; fold together with 1/2 cup of the browned graham cracker crumbs and cooled pudding mixture. Fold in the 2 cups of miniature marshmallows. Pour into a 2 quart serving dish. Reserve 1 Tablespoon of the graham cracker crumbs; sprinkle the remaining browned graham cracker crumbs over the pudding mixture; refrigerate.
Beat the remaining 1 cup of whipping cream and spread over the chilled mixture. Sprinkle the reserved 1 Tablespoon crumbs over the top to decorate. Serve immediately; refrigerate leftovers.