Method

Make the pastry cream (day before)

• In a medium saucepan, bring 1¹⁄₄ cup milk and ¹⁄₃ cup heavy cream just to a simmer
• Meanwhile in a medium mixing bowl
  • Whisk together the egg and 2 egg yolks, ¹⁄₄ cup brown sugar, and 2 tbsp corn starch
  • When ready, slowly whisk in the hot cream
• Transfer back to the sauce pan
• Return the pan to heat and keep whisking until thickened
• Remove from heat and whisk in 4-6 tsp rum, 1 tsp vanilla, lemon zest
• Let cool to room temp
• Cover in contact with plastic and refrigerate if making ahead

Make the cake batter

• Bring 3 eggs and 2 sticks butter to room temperature
• In a small mixing bowl, whisk together 280g flour and 1 tsp baking powder
• In a stand mixer with the paddle attachment
  • Cream together 2 sticks butter, 160g brown sugar, 125g almond flour, 1 tsp salt, and 1 tsp vanilla
  • Beat in the 3 eggs 1 at a time
  • Continue until very fluffy
  • Scrape down the sides and add in the flour
  • Mix on low until just combined

Build the cake

• Butter a 9″ round cake pan and line with parchment (and butter the top of that as well)
• Transfer the cake batter into a piping bag with a 1/2″ circle tip
• Transfer the pastry cream into a piping bag with as big as big of a tip as you have
• Pipe a disk of batter on the bottom of the cake pan
• Pipe a ring of batter on top of that disk, around the inside perimeter of the pan to hold the filling
• Pipe the pastry cream into the middle of the cake
• Pipe another disk of batter on top
• Cover with plastic wrap and smooth the top with your hand
• Refrigerate until firm
• Brush cake top (twice?) with egg wash and score it in a pattern

Bake and finish

• Bake at 350°F for 45–50 minutes
• Let cool for 20 minutes before unmolding
• Transfer to a cooling rack to cool completely
• Serve at room temperature
• Store in the refrigerator