We present the challenges encountered and solutions we reached while converting the TESScut application to run in the cloud. TESScut is a web application that provides image cutouts of chronologically-stacked TESS full-frame images, without requiring the user to work with the image stacks themselves. While running inside our on-premises datacenter, the application ran on a large virtual machine: 32 cores, 64 GB of memory, and nearly 400 TB of high-performance local-storage for serving the image stack data. This single machine served terabytes of cutout request data to users each month. Replicating this specific environment in the cloud would have been prohibitively expensive and beyond our budget. Instead, our cloud architecture utilizes serverless tasks inside AWS ECS Fargate, performs cutouts from remote files on an open data S3 bucket, and relies heavily on autoscaling, to achieve our performance goals while keeping costs within budget. We hope that others can benefit from our experiences and lessons learned.