In the heatproof bowl of a stand mixer, whisk together egg whites and sugar by hand. Heat over a saucepan of simmering water, whisking frequently, until an instant-read thermometer registers 160°F (71°C), about 2 minutes.

Carefully return bowl to stand mixer. Using the whisk attachment, beat at high speed until thickened and cooled to room temperature, 3 to 5 minutes. With mixer on medium-high speed, add butter, 1 tablespoon (14 grams) at a time, beating until combined after each addition. With mixer on medium speed, beat in almond extract, salt, and vanilla. Beat until buttercream comes together and is thickened. (Buttercream may look curdled at first, but keep mixing and it will soon emulsify.) Use immediately, or refrigerate in an airtight container for up to 1 week; when ready to use, let come to room temperature, and beat in a stand mixer fitted with the whisk attachment at high speed until fluffy.