David Dorsey wrote a thoughtful JETS article on the Mosaic law and the Christian in 1991:
Dorsey, David A. “The Law of Moses and the Christian: A Compromise.” JETS 34 (1991): 321–34.
Justin Taylor summarizes that essay in Q&A format here.
In 1999 Dorsey wrote another journal article on the Mosaic law and the Christian. This essay is not as well-known, and it was challenging to track down. I’m uploading an unmarked PDF of the essay here with the publisher’s permission:
Dorsey, David A. “The Use of the OT Law in the Christian Life: A Theocentric Approach.” Evangelical Journal 17, no. 1 (1999): 1–18.
Related: I think this is the best all-around book on Christians and the law:
Schreiner, Thomas R. 40 Questions about Christians and Biblical Law. 40 Questions. Grand Rapids: Kregel, 2010.
Tom Schreiner has focused his scholarly writing on the law since defending his PhD dissertation on circumcision at Fuller Theological Seminary in 1983. Since then he has written many articles and books on Paul and the law, including commentaries on Romans and Galatians, a Pauline theology, and a New Testament theology. So this book is the fruit of about thirty years of deeply reflecting on this issue, and you can tell. It’s clear, concise, and mature.