This is possible!

1. Create a task and choose the last option, "Set Repeating Interval."
2. Set the repeat mode to "From completion date."
3. Set the repeating interval to 1 hour. (Setting it zero causes issues.)

Whenever the task is completed, the start date will be set to one hour from the current time. To see all the start dates (last completion dates), use the “Table” type view in the Project or Saved Filter. In the top-right, you can adjust which columns are shown. Choose to show the Start Date.

You may need to adjust the date format in the settings so it is “Relative (e.g. 3 days ago)” rather than the exact date.