With help from a teammate, I completed an ARM Template and PowerShell script to deploy a Cosmos API Connection for a Logic App to Azure.
Thought I would share with everyone, in case you are curious on how to accomplish this.
Download these two files and navigate to the directory and run the following script in a terminal window:
.\LogicAppCosmosConnection.ps1 -ResourceGroupName "YOUR_RESOURCE_GROUP_NAME" -CosmosAccountName "YOUR_COSMOS_ACCOUNT_NAME"
That’s it!