Preheat oven to 350 degrees F. and line an 8-inch square pan with parchment so that it hangs over the sides (do not grease).
Whisk eggs and sugar over a pot of gently simmering water for about 3 minutes, so that the eggs are just warm to the touch. Remove from heat and whip mixture with electric beaters or in a stand-up mixer until pale yellow, glossy and firm, about 10 minutes.
Sift flour and salt, and gently but quickly fold into eggs in two additions. Combine melted butter, vanilla, zest and juice. Stir about 1/3 cup of cake batter into melted butter until smooth, then sir mixture into cake batter (this will keep the butter from sinking to the bottom).
Scrape batter into prepared pan and bake for 30 minutes, or until cake springs bake when gently pressed. Allow cake to cool for 20 minutes, then turn out onto a cooling rack to cool completely.
For meringue, reduce oven temperature to 250 degrees F. and line a baking tray with parchment paper.
Whip egg whites with cream of tartar until foamy. Gradually add sugar and continue whipping until whites are glossy and hold a stiff peak. Spread meringue onto prepared baking tray into an even layer. Bake for about 40 minutes, or until dry (times may vary depending on air humidity).
For fool, whip cream to medium peaks and stir in remaining ingredients. Break up meringue into pieces and fold into whipped cream.
To assemble, heat tangerine juice and lemon juice with sugar until sugar is dissolved, then remove from heat. Trim outside of cake to remove brown edges and cut into 9 squares, placing each square onto a plate. Brush each square with tangerine syrup. Top each square with a generous dollop of fool and garnish with a tangerine slice. Serve immediately.