Many big data systems are written in languages such as C, C++, Java, and Scala to process large amounts of data efficiently, while data analysts often use Python to conduct data wrangling, statistical analysis, and machine learning. User-defined functions (UDFs) are commonly used in these systems to bridge the gap between the two ecosystems. In this paper, we propose Udon, a novel debugger to support fine-grained debugging of UDFs. Udon encapsulates the modern line-by-line debugging primitives, such as the ability to set breakpoints, perform code inspections, and make code modifications while executing a UDF on a single tuple. It includes a novel debug-aware UDF execution model to ensure the responsiveness of the operator during debugging. It utilizes advanced state-transfer techniques to satisfy breakpoint conditions that span across multiple UDFs. It incorporates various optimization techniques to reduce the runtime overhead. We conduct experiments with multiple UDF workloads on various datasets and show its high efficiency and scalability.