I have been developing Windows Forms programs for few years. I am now looking into .NET Core (including ASP.NET Core MVC). I am searching for the new GUI desktop technology. In Visual Studio 2015 update 3 I can't see any option to make a GUI app in .NET Core.
What am I missing?
You were not missing anything. Microsoft shipped no reasonable way to create GUI applications directly using .NET Core until .NET Core 3, though UWP (Universal Windows Platform) is partially built on top of .NET Core.
.NET Core 3.0 includes support for Windows Forms and WPF, though it is Windows-only.
.NET 6 will include .NET MAUI, which will support Windows and macOS desktop applications and mobile applications, with Linux desktop applications supported by the community (not MS). .NET 5 will include a preview version of .NET MAUI.
For third-party cross platform options, see other answers.