It is quite hard to explain in words so I will show screenshots of what i would like.
This is a screenshot of what happens when I drag with the pen tool.
This is what I would like to happen.
Is there a shortcut to drag out only the first handle?
Sorry this is well past any usefulness to the original poster most likely. I realize this is a very old question. However, this may be helpful to others. This has been a solution in Illustrator since practically it's inception and still works today (CC2018 the most recent version as of this writing).
Hold down the Option/Alt key with the Pen Tool active and click the anchor again, after dragging.
This will set one side of the anchor to a corner while leaving the curve on the other side.
This same method will also function in Photoshop with it's Pen Tool.
Also note in either application, if you hold the Option/Alt and click-drag the open anchor, as opposed to merely clicking, you can create a non-symmetrical corner point.
It's very simple. The trick is start from the right point:
press down -> drag handle -> release mouse btn
and then just one click on the left point.
Here is what i get
Because when using drag to create a point, when this point is a joint, it will be a smooth point by default (2 side control handles). Only when it's a starting point, it will has only one handle.