In the heatproof bowl of a stand mixer, whisk together granulated sugar, egg whites, and brown sugar by hand. Place bowl over a saucepan of simmering water. Cook, whisking occasionally, until an instant-read thermometer registers 120°F (49°C) to 130°F (54°C).

Carefully return bowl to stand mixer. Using the whisk attachment, beat at high speed until stiff peaks form and bowl is cool to the touch, 7 to 8 minutes. Add butter, 2 tablespoons (28 grams) at a time, beating until combined. (If buttercream breaks or looks loose, beat for 2 to 3 minutes, and the emulsion will come back together.) Beat in dulce de leche and orange zest. Use immediately.