I finally figured this out!
The trick was to right click on the Project, go to Properties then select the Debug tab. Next, under Profile, I selected the name of the command defined in my projects.json: "watch". Once selected, I clicked Add by Environment Variables, and added the Name/Value pair ASPNETCORE_ENVIRONMENT and Development.

What this actually does is is upload the launchSettings.json file under Properties in Solution Explorer. This file could also just be edited manually. The output looks something like this:
{
"iisSettings": {
"windowsAuthentication": false,
"anonymousAuthentication": true,
"iisExpress": {
"applicationUrl": "http://localhost:56846/",
"sslPort": 0
}
},
"profiles": {
"IIS Express": {
"commandName": "IISExpress",
"launchBrowser": true,
"environmentVariables": {
"ASPNETCORE_ENVIRONMENT": "Development"
}
},
"LendingTree.CreditCards.Web": {
"commandName": "Project",
"launchBrowser": true,
"launchUrl": "http://localhost:5000",
"environmentVariables": {
"ASPNETCORE_ENVIRONMENT": "Development"
}
},
"Watcher Development": {
"commandName": "Watcher Development",
"launchBrowser": true,
"launchUrl": "http://localhost:5000",
"environmentVariables": {
"ASPNETCORE_ENVIRONMENT": "Development"
}
}
}
}