Everybody knows how to set up a favicon.ico link in HTML:
You can use 8-bit PNG instead of ICO format for even smaller data footprint. Only thing you have to change is using "data:image/png" instead of "data:image/x-icon" MIME type header:
"type" attribute can be "image/png" or "image/x-icon", both works for me.
You can convert ICO to 8-bit png using gimp or convert:
convert favicon.ico -depth 8 -strip favicon.png
and encode PNG binary to base64 string using base64 command:
base64 favicon.png