The Context#cookie method in Javalin is used to return the value of a request cookie by name.
To implement this functionality, you can create a new Maven project named 'javalin-read-request-cookie-by-name' and update the pom.xml file with the necessary Maven dependencies.
You can define a JsonUtil class to handle JSON serialization and a main application class named App.java to set up Javalin routes for reading request cookies by name.
After building the project and running the application, you can test the API using a tool like curl to verify the functionality.