Preheat oven to 350°F (180°C). Butter and flour 3 (5½×3½-inch) loaf pans. (See Note.)

In the bowl of a stand mixer fitted with the whisk attachment, beat eggs, sugar, and vanilla at medium-high speed until thick, pale, and doubled in volume, about 5 minutes. Reduce mixer speed to medium. Add melted butter in a slow, steady stream until combined. (It’s important to add the butter very slowly. If added quickly, the air whipped into the egg mixture will deflate.)

In a medium bowl, whisk together flour, baking powder, and salt. With mixer on low speed, gradually add flour mixture to egg mixture, beating just until combined. Divide batter among prepared pans.

Bake until a wooden pick inserted in center comes out clean, 25 to 30 minutes.

Meanwhile, in a liquid-measuring cup, whisk together condensed milk, evaporated milk, cream, espresso, and liqueur until well combined.

Remove cakes from oven; using a wooden skewer, immediately poke holes about ¼ inch apart into cakes, piercing through to bottom. Immediately pour ¼ cup milk mixture over each cake, allowing mixture to soak into cakes. Divide remaining milk mixture among cakes. Let cool in pans for 1 hour. Wrap pans in plastic wrap, and refrigerate until ready to serve.

Just before serving, use a small of set spatula to loosen cakes from sides of pans; remove from pans. Using a serrated knife, remove rounded tops from cakes. Place Meringue Topping in a piping bag fitted with a jumbo rose tip. (See Note.) Starting at short end of each cake, hold piping bag vertically, and pipe in a zigzag motion down length of cake. Using a kitchen torch, lightly brown Meringue Topping. Serve with coffee syrup.