No, this not some type of healthy sandwich. I have no idea why it is called a Cuban Press. Others call it a Muscle Snatch. This is an exercise that could be classified as a “shoulder saver”. And it’s an exercise that is not going to require a lot of weight to really get those shoulders working.
The first part of the movement is a pull up to about sternum level and then you’re going to externally rotate and extend your arms to bring the barbell overhead. The key is to keep the elbows high as your externally rotating. Take a look: