Preheat the oven to 400, and line two sheet pans with parchment paper. Using a 4” round bowl, trace four 4” circles on each piece of parchment paper. Then, flip the parchment paper over so the pencil side is down (you should still be able to see the tracing lines on the other side).
Place a heavy-bottomed sauce pan (like copper or enamel-coated cast iron) over medium heat. Add the diced butter, water, milk, sugar and salt.
Bring the mixture to a boil, and then remove the pan from the heat. Add all of the flour at once, and stir.
Place the pan back on the stove, and turn the heat to medium-low. Stir the mixture constantly while keeping an eye on the bottom of the pan. After a few minutes, you should see a film on the bottom of the pan after stirring. Remove the pan from the heat.
Add the cooked mixture to the bowl of a stand mixer, fitted with the paddle attachment and let it cool for at least 10 minutes.
After 10 minutes, turn the mixture on for just a minute to break up the dough. Turn it off, and feel the dough with your fingers—it should just be lukewarm, not hot.
Turn the mixer on medium, and begin adding 4 of the eggs, one at a time. Allow the mixture to mix for at least 30 seconds before adding another egg.
After all 4 eggs have been added, the mixture should be glossy and smooth.
Transfer the batter to a large piping bag fitted with a 1/2” round tip.
On the parchment paper, pipe a concentric circle on the inside of the traced circles. When you get to the end, keep going and pipe another circle, butting up against the first circle. THe base of your Paris-Brest is these two concentric circles.
Finally, pipe another circle on top of the two concentric circles, aiming to pipe it exactly where the two circles meet. This is the upper layer.
When all of the circles are done, beat the remaining egg and burns it over the entire surface of each Paris-Brest. Sprinkle the sliced almonds on top.
Transfer the pans to the oven.
After 15 minutes, open the oven door to let out some heat, and turn the oven down to 375. Cover the Paris-Brest on each sheet with an additional piece of parchment paper or foil to keep them from browning too much. Cook for another 20-25 minutes until golden brown.
Once the Paris-Brest is done cooking, remove each pan from the oven, and carefully prick several holes on the tops, sides and bottoms of each pastry.
Return the pans back to the oven with the door ajar, and let the pastries cool in the oven for an hour.
Meanwhile, make the almond-orange buttercream filling: beat the butter until light and fluffy, then add 1 cup of powdered sugar and beat until combined. Add the orange zest, almond extract, and 3 tablespoons of the cream and beat. Add the remaining 2 cups of powdered sugar beat, adding the last tablespoon of cream to help it get going.
Beat until smooth and fluffy.
Scrape the buttercream filling into a pastry bag fitted with a fluted tip.
Using a serrated knife, cut each Paris-Brest in half horizontally to reveal their soft, custardy interiors.
Pipe little mounds of filling on the bottom halves, and top with the Paris-Brest tops.
Sprinkle each Paris-Brest with powdered sugar, and serve.