I've got an option for you, andrewjmakar!
Currently, the recurring invoice feature is offered in QuickBooks Online (QBO). What we do in QuickBooks Self-Employed (QBSE) is we duplicate the existing invoices or we create a draft invoice and duplicate it. Though this will not automatically send them to your customer, at least, you can save time from entering the details on the invoice.
On the other hand, you can find references for QBSE on the QuickBooks Support page. Just choose the QuickBooks Self-Employed topic and click +More Topics below.
If you have other questions about invoices, feel free to go back to this thread.