helm overriding Chart and Values yaml from a base template chart
You may want to read the Subcharts and Global Values doc page within Helm's repo. It covers Creating a Subchart, Adding Values and a Template to the Subchart, Overriding Values from a Parent Chart, Global Chart Values, and Sharing Templates with Subcharts. It sounds like you want the example in Overriding Values from a Parent Chart. Note that all values passed from the parent to the subchart are nested below a YAML key by the same name as the subchart. --set syntax is the same concept, just prefix the key with the subchart name (--set subchartname.subchartkey=myvalue.
Also, docs.helm.sh has good, consolidated Helm documentation, and the Scope, Dependencies, and Values section of Intro To Charts gives more context to the use case above as well as others.