Intuit tells me that I can complete an estate return using Turbotax Premier. How do I start an estate return?

To do a Form 1041 Estate return, you need TT Business.  It is available only as a desktop verison, and then only for Windows.

https://turbotax.intuit.com/small-business-taxes/

Once you issue the K-1 forms, they can be entered in TT Premier for your personal return.