A major security challenge for modern Internet of Things (IoT) deployments is to ensure that the devices run legitimate firmware free from malware. This challenge can be addressed through a security primitive called attestation which allows a remote backend to verify the firmware integrity of the devices it manages. In order to accelerate broad attestation adoption in the IoT domain the Trusted Computing Group (TCG) has introduced the Device Identifier Composition Engine (DICE) series of specifications. DICE is a hardware-software architecture for constrained, e.g., microcontroller-based IoT devices where the firmware is divided into successively executed layers. In this paper, we demonstrate a remote Time-Of-Check Time-Of-Use (TOCTOU) attack on DICE-based attestation. We demonstrate that it is possible to install persistent malware in the flash memory of a constrained microcontroller that cannot be detected through DICE-based attestation. The main idea of our attack is to install malware during runtime of application logic in the top firmware layer. The malware reads the valid attestation key and stores it on the device's flash memory. After reboot, the malware uses the previously stored key for all subsequent attestations to the backend. We conduct the installation of malware and copying of the key through Return-Oriented Programming (ROP). As a platform for our demonstration, we use the Cortex-M-based nRF52840 microcontroller. We provide a discussion of several possible countermeasures which can mitigate the shortcomings of the DICE specifications.