Preheat oven to 250°F (130°C).

In a completely dry 9-inch round cake pan, place white chocolate.

Bake until melted and a light caramel color, about 45 minutes, stirring with a spatula every 10 minutes. (Chocolate might look dry and crumbly at any point but continue stirring until smooth.)

In the heatproof bowl of a stand mixer, whisk together sugar, egg whites, and cream of tartar. Place bowl over a saucepan of simmering water. Cook, stirring frequently, until sugar dissolves and an instant-read thermometer registers 160°F (71°C).

Carefully return bowl to stand mixer. Using the whisk attachment, beat at high speed until mixture has cooled significantly and becomes thick and glossy. Reduce mixer speed to medium-high; add butter, 2 tablespoons (28 grams) at a time, beating until completely combined after each addition. Beat until buttercream is thick and glossy. (It may look slightly curdled at some point, but keep mixing.) Beat in vanilla and salt.

If white chocolate has solidified, transfer to a microwave-safe container, and heat on high in 30-second intervals, stirring between each, until melted. With mixer on medium speed, slowly add white chocolate to buttercream, beating until combined and stopping to scrape bottom and sides of bowl. Use immediately.