Stir together yeast and water in a small bowl; let stand 5 to 10 minutes. Whisk in 2 tablespoons of the oil.
Pulse flour, sugar, baking powder and salt in a food processor a few times to combine. With machine running, pour yeast mixture through feed tube. Start slowly, then pour faster. Process until a dough ball forms, sides of bowl are nearly clean, and dough is medium-soft and tacky but doesn't stick to fingers.
Turn dough ball and bits out onto an unfloured counter and gather into a neat ball. If dough feels stiff, wet hands and knead in the water from your hands. Transfer to an oiled bowl. Cover with cling film and let rise in a warm place until nearly doubled, about 45 minutes.
Meanwhile, cut out 24 (8cm) squares of baking parchment. Put remaining 1 tablespoon oil in a small bowl.
Cut dough in half. Roll one half into a rope, about 4cm thick and 35cm long; cut crosswise into 12 equal pieces. Roll each piece into a ball, then smack it with your palm into a disc about 1cm thick. With a rolling pin, roll each disc into a thin oval, about 6cm wide by 12cm long. Brush half of each oval with oil, then fold in half to form buns.
Set each bun on a parchment square; transfer to a bamboo or metal steamer tray, spacing about 2cm apart and away from steamer walls. Set any that don't fit in the steamer on a baking tray. Loosely cover with a clean drying cloth. Let rise in a warm spot until about 1 1/2 times the original thickness, 20 to 30 minutes.
Meanwhile, fill a steamer pan or a pot halfway with water; bring to the boil over high heat.
Steam buns over boiling water, 2 trays at a time, covered with lid, until puffy and dry-looking, about 8 minutes.
Cooled buns can be chilled up to 3 days in an airtight container or frozen up to 1 month. To refresh, briefly resteam thawed buns or cover with a damp double layer of kitchen roll and microwave in 15- to 20-second bursts.