The best place to start learning about causal inference would be reading Mostly Harmless Econometrics and Mastering Metrics. However recently one of my colleaugues introduced to me Data Analysis for Social Science A Friendly and Practical Introduction by Elena Llaudet and Kosuke Imai. This is an excellent book for undergraduate courses. I have listed below some articles which use which use the causal inference methods which form the bedrock of applied microeconomics.
Difference-in-difference
Card, D., & Krueger, A. B. (1994). Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania. American Economic Review, 84(4), 772–793.
Duflo, E. (2001). Schooling and Labor Market Consequences of School Construction in Indonesia: Evidence from an Unusual Policy Experiment. American Economic Review, 91(4), 795–813.
Synthetic control
Abadie, A., Diamond, A., & Hainmueller, J. (2010). Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program. Journal of the American Statistical Association, 105(490), 493–505.
Abadie, A., & Gardeazabal, J. (2003). The Economic Costs of Conflict: A Case Study of the Basque Country. American Economic Review, 93(1), 113–132.
Cavallo, E., Galiani, S., Noy, I., & Pantano, J. (2013). Catastrophic Natural Disasters and Economic Growth. Review of Economics and Statistics, 95(5), 1549–1561.
This is an article by one of my favourite applied microeconomist Scott Cunningham: Cunningham and Shah - Decriminalizing indoor prostitution Implications for Sexual Violence and Public Health: NBER Working Paper 20281.
Regression discontinuity
Drago, F., Galbiati, R., & Vertova, P. (2009). The Deterrent Effects of Prison: Evidence from a Natural Experiment. Journal of Political Economy, 117(2), 257–280.
Pinotti, P. (2017). Clicking on Heaven’s Door: The Effect of Immigrant Legalization on Crime. American Economic Review, 107(1), 138–168.
Eggers, A. C., & Hainmueller, J. (2009). MPs for Sale? Returns to Office in Postwar British Politics. American Political Science Review, 103(4), 513–533.