gcloud allows you to list organization, folders or projects. I didn't found a option to list projects inside a organization.
Something like:
gcloud projects list --organization=ORG
I think there's no quick way like you mentioned with --organization
arg, but that could be accomplished with, for example, the following UNIX-like script:
for project_id in $(gcloud projects list --format='value(project_id)'); do
org_id=$(gcloud projects describe $project_id --format='value(parent.id)')
if [ $org_id -eq $the_org_you_want_to_find_out ]; then
echo "$org_id > $project_id"
fi
done