Chocolate layer
1. Combine the sugar, espresso, cocoa, cornstarch and salt in a heavy medium saucepan. Whisk in just enough of the milk to make a smooth paste. Whisk in the remaining whipping cream.
2. Bring the mixture to a simmer over medium heat, stirring with the whisk—constantly scraping the bottom, sides and corners of the pot—until the mixture begins to bubble a little at the edges. Continue whisking and cooking for two more minutes.
3. Off heat, whisk in the vanilla and scrape the mixture into a glass or silicone pitcher (for immediate filling) or into the bowl to cool. Next, fill your popsicle molds halfway with your chocolate mixture and freeze for at least six hours.
Vanilla layer
1. In a bowl, stir together the sugar and water until the sugar dissolves. Whisk in the sour cream, milk, cream and vanilla.
2. Take your chocolate popsicles out of the freezer and fill the remaining half with your vanilla side. If your mold has a cover with openings for sticks, cover and insert sticks. Otherwise, freeze until the mixture is thick enough to hold a stick upright and then insert sticks. Freeze until hard, about 4 hours if the mixture was cool, 6 or more hours if hot.
3. Line a tray with wax paper. Fill a container with warm water deep enough to dip the full height of your molds. Dip the mold long enough to release the popsicles when you pull on the stick. Remove and set popsicles on wax paper. Wrap each in a piece of wax paper and/or put them in a resealable plastic freezer bag and return them to the freezer until serving.