Pour water to a depth of 1 1/2 inches in a large saucepan; bring water to a boil over high. Reduce heat to low, maintaining a gentle simmer. Whisk together egg whites, sugar, and salt in bowl of a heavy-duty stand mixer. Crumple a large piece of aluminum foil; shape into a ring about 2 inches high. Place in simmering water in saucepan. (The foil ring will prevent the mixer bowl from touching the water.) Place mixer bowl on foil ring. 

Cook egg white mixture, whisking constantly, until mixture registers 160°F on an instant-read thermometer, 10 to 12 minutes. Transfer bowl to heavy-duty stand mixer fitted with whisk attachment. Beat mixture on low speed for 1 minute; gradually increase speed to medium-high, beating until mixture is fluffy, glossy, and completely cool, 8 to 10 minutes total.

Reduce speed to medium-low, and add softened butter a few pieces at a time, beating well after each addition. Beat in vanilla and almond extracts. Remove whisk attachment; attach paddle attachment. Scrape down sides of bowl with a rubber spatula. Beat frosting on low until very smooth, 1 to 2 minutes. Use immediately, chill in an airtight container up to 3 days, or freeze up to 1 month. (Before using, let chilled or frozen buttercream come to room temperature and beat on low speed.)