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Intel SGX promises powerful security: an arbitrary number of user-mode enclaves protected against physical attacks and privileged software adversaries. However, to achieve this, Intel extended the x86 architecture with an isolation mechanism approaching the complexity of an OS microkernel, implemented by an inscrutable mix of silicon and microcode. While hardware-based security can offer performance and features that are difficult or impossible to achieve in pure software, hardware-only solutions are difficult to update, either to patch security flaws or introduce new features. Komodo illustrates an alternative approach to attested, on-demand, user-mode, concurrent isolated execution. We decouple the core hardware mechanisms such as memory encryption, address-space isolation and attestation from the management thereof, which Komodo delegates to a privileged software monitor that in turn implements enclaves. The monitor's correctness is ensured by a machine-checkable proof of both functional correctness and high-level security properties of enclave integrity and confidentiality. We show that the approach is practical and performant with a concrete implementation of a prototype in verified assembly code on ARM TrustZone. Our ultimate goal is to achieve security equivalent to or better than SGX while enabling deployment of new enclave features independently of CPU upgrades. The Komodo specification, prototype implementation, and proofs are available at https://github.com/Microsoft/Komodo.