Current methods for few-shot fine-tuning of pretrained masked language models (PLMs) require carefully engineered prompts and verbalizers for each new task to convert examples into a cloze-format that the PLM can score. In this work, we propose PERFECT, a simple and efficient method for few-shot fine-tuning of PLMs without relying on any such handcrafting, which is highly effective given as few as 32 data points. PERFECT makes two key design choices: First, we show that manually engineered task prompts can be replaced with task-specific adapters that enable sample-efficient fine-tuning and reduce memory and storage costs by roughly factors of 5 and 100, respectively. Second, instead of using handcrafted verbalizers, we learn new multi-token label embeddings during fine-tuning, which are not tied to the model vocabulary and which allow us to avoid complex auto-regressive decoding. These embeddings are not only learnable from limited data but also enable nearly 100x faster training and inference. Experiments on a wide range of few shot NLP tasks demonstrate that PERFECT, while being simple and efficient, also outperforms existing state-of-the-art few-shot learning methods. Our code is publicly available at https://github.com/facebookresearch/perfect.git.