Related to this, so pardon my pitch:
We [Azure] literally just launched Azure Container Registry Build. [1]
With one command you can build your container in the cloud and have it stored in your registry. Either push the source code from local or have it use a remote git repository.
> $ az acr build --registry $ACR_NAME --image $IMAGE_NAME:$TAG_NAME --context .
[1] https://docs.microsoft.com/azure/container-registry/containe...