Stop Visual Studio from launching a new browser window when starting debug?
Open your startup project's properties (Project → {ProjectName} Properties... from the main menu or right click your project in the Solution Explorer and choose Properties), then navigate to the Web tab and under Start Action choose Don't open a page. Wait for a request from an external application.
You will still be able to use any browser (or Fiddler, whatever) to access the running application, but it won't open the browser window automatically, it'll just start in the background and wait for any requests.
For VS 15.7.1 Tools → Options → Projects and Solutions → Web Projects → uncheck Stop debugger when browser window is closed.
Updated answer for a .NET Core Web Api project...
Right-click on your project, select "Properties," go to "Debug" and untick the "Launch browser" checkbox (enabled by default).
