Automated essay scoring (AES) has advanced significantly with neural language models, yet most systems remain opaque, offering little visibility into how grades are produced. In educational settings, instructors must be able to understand, trust, and occasionally override the automated grading decisions. We introduce EssayCBM, a rubric-aligned concept bottleneck framework that decomposes essay evaluation into eight interpretable writing concepts before computing the final score. Unlike direct LLM-based grading approaches, EssayCBM learns an explicit and auditable mapping from writing concepts to grades, allowing instructors to inspect and adjust rubric-level predictions during grading. EssayCBM matches neural AES baselines while making grading decisions transparent and directly editable at the rubric level. We further present an interactive system that demonstrates this capability by allowing instructors to inspect and modify concept predictions in real time.