One variation of an apparatus for brewing a beverage includes: a reservoir containing fluid; a boiler including a heating element and a fluid pickup, a portion of the boiler arranged vertically below the reservoir; a brew chamber, a portion of the brew chamber arranged vertically above the boiler; a first contactless valve operable in a first mode and in a second mode, the first contactless valve open in the first mode to communicate fluid from the reservoir into the boiler and closed in the second mode; a second contactless valve operable in the first mode and in the second mode, the second contactless valve open in the first mode to vent gas from the boiler and closed in the second mode; and an air pump configured to displace air into the boiler in the second mode to displace fluid from the boiler, via the fluid pickup, into the brew chamber.