Development economics papers that used Difference-in-Differences
A very good paper that I had in my MA curriculum is Jaychandran and Pande, AER 2017: https://www.aeaweb.org/articles?id=10.1257/aer.20151282 (I believe this paper has open access, maybe on one of the authors' websites).
Working through this paper should help you understand DID quite thoroughly. The paper also employs double and even triple DID.