How to recurse through a directory tree to find files with Powershell

Now, before you throw out the super simple answer of Get-ChildItem -Recurse, here is my unique issue:

I am connecting remotely to Azure with Powershell, grabbing the site (slot) list, then looping over the sites and finding all images in the directory structure, using Kudu API. Since Kudu has no notion of recursion, I have to build my own recursive function to grab all images from the root directory, then recurse through all children and chidren's children, etc, to also find the image files in those directories.

Here is my code for connecting to Azure and grabbing the root directory:

function Get-AzureRmWebAppPublishingCredentials($resourceGroupName, $webAppName, $slotName = $null){
    if ([string]::IsNullOrWhiteSpace($slotName)){
        $resourceType = "Microsoft.Web/sites/config"
        $resourceName = "$webAppName/publishingcredentials"
    }
    else{
        $resourceType = "Microsoft.Web/sites/slots/config"
        $resourceName = "$webAppName/$slotName/publishingcredentials"
    }
    $publishingCredentials = Invoke-AzureRmResourceAction -ResourceGroupName $resourceGroupName -ResourceType $resourceType -ResourceName $resourceName -Action list -ApiVersion 2015-08-01 -Force
        return $publishingCredentials
}


function Get-KuduApiAuthorisationHeaderValue($resourceGroupName, $webAppName, $slotName = $null){
    $publishingCredentials = Get-AzureRmWebAppPublishingCredentials $resourceGroupName $webAppName $slotName
    return ("Basic {0}" -f [Convert]::ToBase64String([Text.Encoding]::ASCII.GetBytes(("{0}:{1}" -f $publishingCredentials.Properties.PublishingUserName, $publishingCredentials.Properties.PublishingPassword))))
}

function Fill-MimeTypes(){
    return @("image/gif", "image/x-icon", "image/jpeg", "image/png", "image/tiff", "image/bmp")
}

$MimeTypes = Fill-MimeTypes
[System.Collections.ArrayList]$Directories = @()


#Login to Azure Account
Login-AzureRmAccount

#Get the Azure subscription
Select-AzureRmSubscription -SubscriptionName [Subscription Name]

#Get the resource group name
$resourceGroupName = [Resource Group Name]

#Get the WebApp name
$Resources = Find-AzureRmResource -ResourceType Microsoft.Web/sites -ResourceGroupNameContains $resourceGroupName

ForEach($Resource in $Resources)
{
    #Get the WebAppName
    $WebAppName = $Resource.Name

    #Now, get the publishing creds
    $publishingCredentialsHeader = Get-KuduApiAuthorisationHeaderValue $resourceGroupName $WebAppName $null
    $ApiUrl = "https://$WebAppName.scm.azurewebsites.net/api/vfs/site/wwwroot/"

    #Now get the list of files in the wwwroot directory
    $InitialList = Invoke-RestMethod -Uri $ApiUrl -Headers @{Authorization=$publishingCredentialsHeader} -Method GET -ContentType "application/json"

    ForEach($Item in $InitialList)
    {
        If($MimeTypes -Contains $Item.mime)       
        {
            #Add image file data to a collection
        }

        If ($Item.mime -eq "inode/directory")
        {
            #So, here is where I need to recurse...
            #The mime type of inode/directory means it's a directory ;)
            #I now need to call the Api again with the Url and get the contents of the current directory and rinse and repeat until done
            #But I cannot forget about the other directories in the root directory and their children.
        }
    }
}

How can I write the recursive function?