Please see the attached image.
Questions asking effects which simulate old manual image print plate making techniques like metal engraving or wood cutting appear now and then. The previous one before you was this: Transform an image into parallel lines with varying distance? It got a couple of answers and links to other cases for more perspective.
Engraving effects can make lines which simulate greyshades by varying line widths and line densities, but grooves carved by a talented person have one superior advantage: They seem to follow the curved surface of a 3d object. Lines created by an engraving effect do not follow surface curvature, because the effect sees only the given 2D image, it knows nothing of the 3D forms of the object the image present. A human engraver knows and takes it into the account in the fly (after practicing several years).
I unfortunately have too poor skills to create manually a drawing which imitates properly a manually crafted human portrait engraving, no matter I have Illustrator which allows as many undos and retries as needed and generates smooth curves no matter how much my hands shake. But I can draw a simple enough shape to show the idea, say a simple cardboard mug upside down i.e. a shortened cone.
Top left: The mug as a line drawing - it's 2 lines, an ellipse and a half of an ellipse
Top right: Colored with solid grey and a gradient to simulate light and shadow
Bottom left: Greys are replaced by lines and curves. The curves are splitted from a series of ellipses created with Blending. This is quite poor shading, because it doesn't present at all the gradient from light to shadow. But it presents the surface curvature with only a few lines much more effectively than any engraving effect I have seen.
Bottom right: The shading has got non-uniform line widths by applying a preset line profile. Arbitary profiles can be created in Illustrator by making Art Brushes.
A person with sharp sight and steady hands draws the varying width curves with a drawing tablet which is set to obey the stylus pressure or tilt angle. That happens only if the person has got in the birth what the job needs and developed the skill by making thousands of practicing drawings.