Okay, keep in mind I do Japanese. Chinese is new to me, but I have good online tools.
I have the Douji Shangdou brick.
Douji is 斗記; these are the symbols written in the ink/grass-style on the front of the box (and the "logo" impressed onto the cake).
斗 is a apparently a peck, or liquid measure.
記 means record, or measure
So take your pick of what that means. Measuring liquid.
Shangdou. This took me a little, but it's inscribed on the *end* of the box in red lettering. I'm sure this would be extremely obvious to those who speak Chinese w/o even seeing the characters, because....
Shangdou is 上斗
上 means upper, greater, superior
already covered the other one.
So Shangdou is the superior peck, or most likely just the superior part.
I'd have to see what the characters are for for dadou. Well, we should know what 'dou' is at this point. My guess is 'da' will be 大, which means "great, large, vast."
Hope that helps....