To prepare the mango topping: Slice mangoes lengthwise. Using a spoon, remove flesh from the halves. Cut into half-inch slivers and place into a medium bowl. Sprinkle lemon juice (to give a touch of acidity to the cake and brighten the mango color) on top and set aside.
In a small sauce pan, melt butter over medium heat, then stir in brown sugar. Simmer, stirring, until sugar has dissolved. Without stirring, let cook a little bit more until bubbles start to form around the edges of the mixture (i.e.the sugar begins to caramelize). Spread mixture in the bottom of a buttered 9-inch round baking pan and arrange mango slivers on top in a rose pattern or any other that you wish (Note: It is very important to fill all or most spaces; otherwise topping will not look as pretty as it could (Mine did not have all the spaces filled because only 2 mangoes were used). Then, set aside.
To make the mango upside down cake batter: Preheat the oven to 350 degrees F (177 degrees C). Whisk together the flour, baking powder and salt in a medium bowl and set aside. In the bowl of an electric mixer with a paddle attachment, beat the softened butter and sugar together at medium speed until light and fluffy (about 5 minutes). Add the 2 whole eggs, one at a time, and then the egg yolk -- beating after each addition. Beat in both the vanilla and yogurt.
Add half of flour mixture, beating at low speed until just combined. Mix in mango juice, then add remaining flour mixture, mixing until just combined.
Spoon the batter over the arranged mango slivers in the cake pan (Be careful not to disturb the mango pattern!!!) and then, spread the batter smooth and even. Bake for 33-37 minutes (dark pan) or 45 - 50 minutes (shiny pan) or until golden brown and a toothpick inserted in the center comes out clean.
Let cool on a wire rack for about 10 minutes. To unmold the mango upside down cake, run a thin knife gently along the edges of the pan, invert onto a platter, and continue cooling. If desired, garnish top of the mango upside down cake with pomegranate seeds (optional). Serve mango upside down cake slightly warm or at room temperature by itself or with ice cream.