Automated cooking robots have traditionally relied on predefined procedures and rule-based control, ensuring stable execution but offering limited personalization, whereas recent large-model approaches support natural language interaction but often suffer from opaque decision making and unreliable execution in real kitchens. To address this challenge, this paper proposes an agentic framework that systematically decomposes personalized cooking requirements into structured and verifiable control programs rather than directly mapping language to actions. Multiple artificial intelligence (AI) agents collaboratively transform user intents into canonical recipes, workflow programs with explicit flow control, and executable Python code grounded in an atomic action library. The system consists of three tightly coupled stages: offline recipe-to-code generation through multiple agents, online closed-loop execution with supervisory intervention enabled by multimodal perception, and post-run adaptation that updates user preference models for long-term personalization. Real-world experiments on a physical cooking platform demonstrate that the proposed framework achieves reliable task completion, transparent execution logic, and effective anomaly handling across diverse personalized scenarios, validating its practicality for trustworthy automated cooking in real environments.