In a medium saucepan, combine 1 cup cream and sugar. Split the vanilla bean lengthwise and scrape out the middle and drop that into the pot. (Throw your leftover vanilla bean pod into your sugar jar. You will have wonderful vanilla sugar.) Cook cream mixture over medium heat, stirring constantly until the sugar is completely dissolved. Remove from heat.
In a large bowl, combine the rest of the cream, the milk, and vanilla extract. Pour in the hot cream and sugar mixture. Stir to combine. Cover by pressing plastic wrap directly onto the mixture and refrigerate until completely cool, preferably overnight. (The cooler the cream, the easier it is for the ice cream maker to make, which leads to more consistent sized crystals which equals better mouthfeel).
The next day, chop cup your Reese's cups and throw them in the freezer for 20 minutes or so. This helps prevent them from being totally crushed. While you are waiting, make the chocolate sauce or if you are using your favorite store bought brand of chocolate sauce, scroll through Instagram.
Churn ice cream according to manufacturer's instructions. During the last 5 minutes of churning, toss in the Reese's cups and chocolate chips.
In your final ice cream container (the one that is going into the freezer), drizzle chocolate sauce on the bottom and sides of the container. Scoop 1/4 of ice cream into container. Drizzle with more chocolate sauce. Scoop more ice cream on top, drizzle more sauce. Repeat until all the ice cream is used. Freeze for a couple more hours until firm. When you scoop the ice cream, you will now have chocolate "ribbons" in the ice cream.