When building .NET applications offline, the dotnet restore and build commands don't automatically use locally cached NuGet packages. The workaround involves three steps: locating the local NuGet cache with `dotnet nuget locals all --list`, adding the global-packages directory as a NuGet source with `dotnet nuget add source`, and specifying an explicit package version when running `dotnet add package`. This allows developers to build .NET apps without an internet connection using previously downloaded packages.