Preheat the oven to 350°F (175°C).
Grease two 8-inch round baking pans with butter. Set aside.
Cream the butter using a stand or hand mixer. Add the sugar slowly and continue beating until the butter turns pale yellow and creamy.
Pour the eggs into the mixer one at a time, beating after each addition until all of the eggs are well incorporated.
Sift the flour, baking powder, and salt together in a separate bowl.
Slowly add the flour mixture to the mixer alternating with the orange juice and vanilla. Add the orange peel and continue to mix until all ingredients incorporate. Do not overmix the batter.
Transfer the batter to the baking pans adding half of the batter to each pan. Bake for 35–40 minutes, or until a toothpick inserted in the center comes out clean.
Remove from the oven and let it cool completely on a cooling rack before filling and frosting.
To make the frosting
Mix sugar and water in a medium saucepan. Boil over medium heat for about 20–30 minutes, or until it reaches the consistency of syrup. To know if the syrup is ready, insert a spoon into the syrup and lift it up. If it drips in a consistent stream that looks like a thread, the syrup is ready. It’s important that the syrup is at the point or your meringue won’t have the right consistency.
About 4–5 minutes before the syrup is ready, start beating the egg whites and cream of tartar in a stand mixer using the wire whisk attachment on low speed. Increase the speed to high and continue beating until the egg whites start to form soft peaks.
Pour the syrup into the mixer in a slow stream, while beating the egg whites on high speed. Continue beating the meringue for about 5–8 minutes, or until the temperature has cooled and stiff peaks begin to form.
Mix in the vanilla extract and lime juice. Continue beating the meringue for an additional 5 minutes, or until the temperature has cooled down completely, strong peaks form, and the meringue has a glossy shine.
To assemble the cake
Cut the cake tops to level the cake and make them even. Place one of the cakes in a cake stand or a flat plate.
Fill a piping bag with meringue and make an outer circle on top of the cake with it. Spread dulce de leche filling evenly in the center. Place the second cake on top.
Spread meringue evenly on top and around the cake. Decorate as desired.