Tong Kee Bao Dim (Hong Kong)
With most places in Hong Kong, it's hard to feel 100% confident regarding allergies, but a friend recommended simple foods. While many bakeries are rife with sesame and dairy, mantou (steamed white bread buns) usually doesn't have any of these, so may be an option. Just be sure to get the plain ones (nothing filled with custard if you are allergic to dairy!), and be conscious of cross-contamination (as they do make other buns with sesame) as allergies to sesame aren’t as common or well understood in Hong Kong.
11 Canal Rd W, Wan Chai, Hong Kong