Modern embodied agents achieve impressive performance, but their task knowledge is often stored in neural weights, latent state, or prompt-bound memory, making individual policy knowledge difficult to inspect, validate, recombine, and reuse. We introduce \textbf{Kintsugi}, a white-box policy-learning framework that treats embodied policy improvement as verifier-gated construction of a typed executable Knowledge Base (KB). Kintsugi represents task-level policy knowledge as composable typed entries -- predicates, operators, policy schemas, monitors, recovery rules, experience records, and goals -- and improves this artifact through localized typed edits induced from rollout evidence, rather than relying on test-time language-model reasoning. Between rollouts, a tool-constrained agentic editing loop diagnoses trajectory failures, localizes them to editable KB layers, and proposes candidate edits. A deterministic verification gate admits an edit only when the candidate type-checks, the resulting KB executes, and focused validation success or trajectory-health metrics improve without violating protected-regression checks. At inference, the accepted KB is executed by a deterministic symbolic executor with zero LLM calls. Across long-horizon text-agent benchmarks and representative object-centric manipulation settings, Kintsugi achieves strong endpoint performance while preserving inspectability, local editability, and verifier-gated deployment. These results suggest that embodied policy improvement can be organized around executable task knowledge.