Is there a way in Premiere to process a file like logging and capture?
Try this:

Create a bin in your project window, lets call it "selected-clips".

Use your source window to mark your "in and out" points then drag that 'clip' into your "selected-clips" bin.

Once you have all your clips in, right-click on EACH clip and select "Make Subclip".

Now, highlight all the 'Subclips', right-click and select "Export Media". A window should appear - add it to a queue - Media Encoder should open - then batch export your 'Subclips'.

Done.