Log parsing aims to extract log events from massive system log data, which is a key initial step for many tasks such as log compression, anomaly detection, failure diagnosis, etc. With the development of LLMs, leveraging the key text understanding and summarizing abilities of LLMs has been proven to be an effective way for accurate log parsing. Existing LLM-based methods mainly focus on the constant part of logs, ignoring the untapped potential of log variables, resulting in inefficient sampling, cache utilization, and context learning. To address these issues, we demonstrate a new log parsing strategy called the variable-centric strategy named \name that explores the potential of log variables through dynamic contribution sampling, variable-centric parsing cache, and adaptive variable-aware ICL. Early experiments show that it enhances parsing efficiency and substantially reduces the cost of large language model (LLM) calls.