For learning and practice, I did a "mill-ed" groove on a half cylinder.
There may be better or more simple ways?

Making a rectangular "milled" groove on or into the surface of a solid. The surface can be curved.

This is just an off the cuff summary of (all or most of) the steps that I used.

Object to be milled is half of a cylinder.
"Milled" region is based upon an initial planar rectangle profile curve, but could be a circle, or other closed curve. The milled region is a narrow-ish groove, with shallow-ish depth.
(Or the whole rectangular area could be milled out)

Place the rectangle profile curve in front of the rounded surface of the cylinder.
Duplicate the rectangle with an offset rectangle.
(I used FatLines script by Max, to make two new nested rectangles, and discarded initial profile, but other techniques will work.)

Project the two nested rectangles onto the rounded surface of the cylinder. This produces two new curved "rectangles" curves. Use these to trim the surface of the cylinder into a "picture frame" surface. As Michael mentions, extrude the curved rectangles into the half cylinder.
Move the "picture frame" to the bottom of the extruded depth of the extrusions. Join up the relevant parts, to yield a half cylinder with a "milled" groove.
I avoided the seam of cylinder. Have not investigated Seam effect of cylinder.

(Edit: trim can be used instead of projection, as per Michael's links. The picture frame can be extruded, with set dir, instead...Then boolean(?))

- Brian
After viewing Michael's links, there seem to be various ways to extrude various objects, for a variety of different results. Set dir helped for some ways...
So folks may have different solutions to the problem of milling?
Some kind of Macro script might be nice?

I'll delete the attachment in a few days.