After doing the above steps once, opening the Browser from the menu again and noticing that oddity above, I closed the browser. When I went to open the Browser using the menu entry, Tear popped up so I closed it.
$ dbus-monitor [snip] method call sender=:1.35 -> dest=org.freedesktop.DBus serial=291 path=/org/freedesktop/DBus; interface=org.freedesktop.DBus; member=StartServiceByName string "com.nokia.osso_browser" uint32 0 [snip] $ dbus-send --session --print-reply --type=method_call --dest=org.freedesktop.DBus /org/freedesktop/DBus org.freedesktop.DBus.GetConnectionUnixProcessID string:":1.35" method return sender=org.freedesktop.DBus -> dest=:1.535 reply_serial=2 uint32 1123 $ ps -ef | grep 1123 1123 user 108m S /usr/bin/hildon-desktop