Mixture-of-Experts (MoE) has emerged as a promising architecture for modern large language models (LLMs). However, massive parameters impose heavy GPU memory (i.e., VRAM) demands, hindering the widespread adoption of MoE LLMs. Offloading the expert parameters to CPU RAM offers an effective way to alleviate the VRAM requirements for MoE inference. Existing approaches typically cache a small subset of experts in VRAM and dynamically prefetch experts from RAM during inference, leading to significant degradation in inference speed due to the poor cache hit rate and substantial expert loading latency. In this work, we propose MoEpic, an efficient MoE inference system with a novel expert split mechanism. Specifically, each expert is vertically divided into two segments: top and bottom. MoEpic caches the top segment of hot experts, so that more experts will be stored under the limited VRAM budget, thereby improving the cache hit rate. During each layer's inference, MoEpic predicts and prefetches the activated experts for the next layer. Since the top segments of cached experts are exempt from fetching, the loading time is reduced, which allows efficient transfer-computation overlap. Nevertheless, the performance of MoEpic critically depends on the cache configuration (i.e., each layer's VRAM budget and expert split ratio). To this end, we propose a divide-and-conquer algorithm based on fixed-point iteration for adaptive cache configuration. Extensive experiments on popular MoE LLMs demonstrate that MoEpic can save about half of the GPU cost, while lowering the inference latency by about 37.51%-65.73% compared to the baselines.