[jfaucett]

It depends on the degree of quantification and your precise definition of software engineering, but IMHO almost all of software engineering research is minimally as quantitative as the social sciences i.e. psychological or sociological studies and analyses. In other areas, as you also mention, SE is almost purely quantitative in nature.

see: https://jserd.springeropen.com/, https://research.google.com/pubs/SoftwareEngineering.html, and https://arxiv.org/list/cs.SE/recent for some recent SE research topics.

Software Engineering encompasses, broadly speaking, the following topics:

Software Design => Implementation => Testing & QA => Automation => Project Management

Implementation, Testing/QA, and Automation are largely very quantitative, you can create models and algorithms and analyze them and measure most things even easier than in the physical sciences. On the other hand, due to the nature of Software Design and Project Management you are largely left to tools of the social sciences i.e. surveys, difficult to control experiments, observations, etc.