I passed part 1 yesterday and am now beginning part 2 (with the intention of finishing before the deadline at the end of July).
When I went to purchase the assignment at pearsonvue.com, I found the navigation somewhat confusing. I looked for 1Z0-865, but found only 1Z0-864 and 1Z0-866 in the main list of exams. Nothing I noticed made mention of downloadable assignments, but I found the navigation guidance at Oracle's certification blog (right here).
* Under Non-Proctored, select 'Master Assignment' to purchase the assignment. (NOTE: this option is not available before June 1)
Follow the instructions in the system to complete your assignment/essay purchase.
Upon completing registration, you will be given instructions on how to download your assignment.
After vending 1Z0-865, the purchasing interface presents a receipt that includes a yellow "Begin Exam" button. Clicking that button leads to a simple browser-based download manager where you can click one button to download and another to "pause" the "exam" until you're ready to upload a submission.
I thought I'd explain this in case anyone else experiences the same uncertainty about how to get the assignment.