From AWN Wiki

[edit] Info

The Epiphany plugin displays the current page's favicon on Awn.

[edit] Installation

Download both files from here (scroll down). Place them in either ~/.gnome2/epiphany/extensions/ to install just for yourself, or /usr/lib/epiphany-gecko/2.x/extensions/, where 2.x is your version of Epiphany, to install system-wide.