<p>If I have a 3D cylindrical extrusion (in Onshape), how can I scoop, carve, or indent a concave/parabolic curve in one of the ends?</p>

<p>The yellow surface is the target.
<a href="https://i.stack.imgur.com/80wQB.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/80wQB.jpg" alt="Object"></a>
Here is the basic shape I'm trying to bore out (like a satellite dish, parabolic antenna, or even a contact lens.. You get the idea).
<a href="https://i.stack.imgur.com/cbthB.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/cbthB.jpg" alt="Void"></a></p>

As is typical with many CAD type programs, a feature in Onshape known as revolve may be your solution. As you have a clear formula for the cross-section, half of the work is complete.
You would generate a sketch representing the curve, then use the Revolve feature with the axis oriented to vertical. According to the
Onshape video
, you can generate a solid or a surface from the options that appear when selecting that feature.
As you can see in the images above, the axis selected in the tutorial video is horizontal. Other features of revolve are covered in the video. Your post suggests it will also be necessary to perform a subtraction action on the assembly in order to get the scoop/concave result.