In a large bowl, combine the whipping cream, sweetener, and vanilla extract. Beat until it hold stiff peaks.
Remove about 1/3 of the whipped cream to another bowl and reserve. Whisk in the flat root beer and the root beer extract, if using.
Dollop whipped cream into the bottom of each of the popsicle molds. It doesn't need to be perfect, streaks make it fun. Gently tap the molds on the counter to get the whipped cream to the bottom.
Pour the root beer mixture into the molds. Freeze one hour, then push wooden popsicle sticks 3/4 the way into each popsicle. Continue to freeze until firm, at least another 3 hours.
To release the popsicles, heat up water in a kettle. Stand over the sink and pour hot water on the outside of the mold for about 5 seconds (for each popsicle that you want to remove). Gently tug the wooden stick to release.