Tea! This post is Uncle-approved!
Toph’s father is drinking tea from a gai wan i.e. a lidded bowl. These kinds of teacups are generally preferred for tea with more delicate aromas, since the lid helps preserve them. The leaves are staying in the cup, the lid is used to keep you from accidentally drinking them.
Image source and more detailed information on how to brew tea using one.
A gai wan 盖碗 is a Chinese lidded bowl used for the infusion and consumption of tea and was invented during the Ming Dynasty. It consists of a bowl, a lid, and a saucer.
Holding
Usually all three parts are held at once with both hands. Hold the saucer with the 4 fingers of your right hand and let your thumb rests on the edge of the bowl. Use your left hand to hold the lid, with which to brush away any tea leaves before bringing the rim of the bowl to your lips. As the liquid is hot it can take some practice doing this.










