Post cathedral you can get an efficient but nonetheless satisfying lunch from (the fast-expanding) Obika Mozzarella Bar in Duomo Plaza. It’s in the Rinascente shopping mall (underground, it ain’t) but it has spectacular views onto the Duomo Cathedral.
La Rinascente Duomo (Shopping Mall)
Floor 7 (Food Market)
via S. Radegonda 1 corner Piazza Duomo Milano
Open daily from 9:30 am to midnight.