The simplest option is to change your currently selected debugger run option (the dropdown with the green "play" button / F5) from IIS, to the name of your project (e.g. so that "FooWebApp" shows up now in the dropdown). This way the browser will still open like it was before, but the console window will start showing as well.
On the other route with Tuvia's answer above (thanks!), it's actually Properties/launchSettings.json
which stores / determines these actions. There you can also set "launchBrowser": false
if wanted, or if you want to change if the console window opens, within "IIS Express"
profile, manually add: "ancmHostingModel": "OutOfProcess"
(or else set to InProcess
).