Before you read my answer: This solution is going to stop the app and cause the application to re-enter the startup in the next request.
.NET Core 2
There may come a time when you wish to force your ASP.Net Core 2 site to recycle programmatically. Even in MVC/WebForms days this wasn’t necessarily a recommended practice but alas, there is a way. ASP.Net Core 2 allows for the injection of an IApplicationLifetime object that will let you do a few handy things. First, it will let you register events for Startup, Shutting Down and Shutdown similar to what might have been available via a Global.asax back in the day. But, it also exposes a method to allow you to shutdown the site (without a hack!). You’ll need to inject this into your site, then simply call it. Below is an example of a controller with a route that will shutdown a site.
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using Microsoft.AspNetCore.Hosting;
using Microsoft.AspNetCore.Mvc;
namespace MySite.Controllers
{
public class WebServicesController : Controller
{
private IApplicationLifetime ApplicationLifetime { get; set; }
public WebServicesController(IApplicationLifetime appLifetime)
{
ApplicationLifetime = appLifetime;
}
public async Task ShutdownSite()
{
ApplicationLifetime.StopApplication();
return "Done";
}
}
}
Source: http://www.blakepell.com/asp-net-core-ability-to-restart-your-site-programatically-updated-for-2-0