The convergence of blockchain and deep learning (DL) drives the intelligence of the Internet of Things (IoT) with security guarantees. However, the soaring resource consumption resulting from blockchain mining and DL model training has overwhelmed the extremely resource-constrained IoT. In this article, we first build a blockchain and DL-empowered cloud–edge orchestrated framework for an extremely resource-constrained IoT environment. To solve the resource bottleneck of this framework, we then propose a Zero-knowledge Proof of Learning (ZPoL) consensus approach to channel the meaningless Proof of Work (PoW) mining energy waste to valuable DL model training, while protecting the DL model privacy. Besides, to encourage resource-constrained IoT devices to perform meaningful DL model mining in our ZPoL consensus, we design a model quality-aware incentive mechanism based on a two-stage Stackelberg game. Moreover, we conduct extensive simulations and experiments to evaluate our proposed ZPoL-based framework. The numerical simulation illustrates that our proposed incentive mechanism could motivate IoT devices to actively join in DL model mining. Compared with the existing blockchain and DL-enabled IoT system, experimental results demonstrate that our proposed ZPoL-based framework could significantly reduce the communication, computation, and storage cost, which is more applicable to a resource-constrained IoT environment.