Constructing assessments of any kind is a learned skill. Here are two resources that offer useful information about designing meaningful assessments.
Mary Piontek, with the University of Michigan’s Center for Research on Learning and Teaching, authored Best Practices for Designing and Grading Exams, a primer on classroom assessment. It’s easily read, and explains the logic and principle of test design, looking at the pros and cons of different kinds of achievement test items. On page five, there’s a section on “General Guidelines for Developing and Scoring Essay Exams” and on page nine, a sample grading rubric for “Critical Papers.” (Such a rubric would be something to build upon for a similar assignment in your class, and building it with students—so that they play a part in developing performance expectations—almost surely would lead to improved performance.)
This resource, Principles of Test Creation: A Self-Instructional Handbook for BYU Educators, offers a variety of examples, ranging from multiple-choice questions to completion questions to ways to assess higher-order thinking.