For the cake: Preheat oven at 180°C/350°F. Grease and flour a round cake pan. Whip together eggs, sugar and vanilla until fluffy. Gently fold in flour using a spatula to combine. Pour the batter into the pan and bake for about 15 minutes. Turn the cake out onto a wire rack to cool completely.
For the meringue: Gently simmer some water in a medium-size pan. Combine all the ingredients the bowl of a stand mixer and cook for 4-5 minutes on a water bath stirring constantly (the bowl must not touch the simmering water) until the sugar is dissolved and it is hot to the touch. Remove from the heat and place the hot bowl back onto the stand mixer. Whisk on high speed until egg whites are cool, glossy and stiff peaks form, about 3-5 minutes.
Assembling: Cut the cake in half horizontally and pour spoonfuls of syrup to moisten it. Spread the bottom half of the cake with dulce de leche and cover with the mini meringues. Spread more dulce de leche on the other half and place it on top, filling side down (as in a sandwich). Cover with the meringue and decorate to taste.