As long as the [Assigned Employee] is a user field, you should be able to select it in a "Reminder" email.
If [Assigned Employee] is an email field, the only "Permission Type" capable of sending to an email field is an "Open" one. Reminders don't have a "Permission Type" setting, so I don't think this is possible.
If that is the case, a solution could be to create a table that holds a recipient (email field), subject (text field), and body (Rich Text Field) and then set up a pipeline that will create a new record based on the trigger you defined.
You could then configure a "Open" notification to send to the email in [Recipient] whenever a record is created in that table.
Basically, your own little notification engine built on Pipelines.