Preheat oven to 400°. Line 3 rimmed baking sheets with parchment paper. Using a pencil, draw 20 (2 3⁄4-inch) circles on parchment paper; turn parchment over.
In a medium saucepan, melt butter over medium heat. Add 1⁄2 cup water, milk, granulated sugar, and 1⁄2 teaspoon salt, stirring to combine. Bring mixture to a boil. Remove from heat, and stir in flour. Return to medium heat, and cook, stirring constantly, until a skin forms on bottom of pan.
Transfer mixture to the bowl of a stand mixer fitted with the paddle attachment. Let cool for 3 minutes. With mixer at low speed, add 4 eggs, one at a time, beating well after each addition.
Transfer dough to a piping bag fitted with a small round tip (Wilton #12). Using even pressure, pipe a circle onto parchment paper around inside of one of the drawn circles. Once you have completed a full circle, move your tip inward and pipe a second circle, abutting the first. Pipe a third circle on top of the crevice where the first two rings meet. Repeat the same piping technique for the remaining pastries.
In a small bowl, whisk together remaining 1 egg and remaining 1⁄8 teaspoon salt. Using a pastry brush, lightly brush pastries with egg wash. Sprinkle with almonds.
Bake until lightly puffed and golden brown, approximately 15 minutes. Reduce oven temperature to 375°. Bake until fully puffed and golden brown, approximately 10 minutes more, covering with foil to prevent excess browning, if necessary.
Using a wooden pick, carefully poke holes in top and sides of pastries to release excess moisture. Turn oven off, and let pastries remain in oven with door cracked for 1 hour to cool completely.
Using a serrated knife, cut pastries in half horizontally.
Place Orange Buttercream in a pastry bag fitted with a large open-star tip (Wilton #1M). Pipe a decorative border inside bottom half of pastries. Cover with top half of pastries. Dust with confectioners’ sugar.
Recipe by TeaTime Magazine at https://teatimemagazine.com/paris-brests/