Slice the ripe mangoes lengthwise and use a spoon to remove the flesh from the halves. Cut the mango flesh into half-inch slivers and place them into a medium bowl. Sprinkle the juice of half a lemon or lime over the mango slices to add acidity and keep the color vibrant. Set aside.

In a small saucepan, melt the unsalted butter over medium heat, then stir in the packed light brown sugar. Simmer and stir until the sugar dissolves. Allow the mixture to cook without stirring until small bubbles begin to form around the edges (the sugar will begin to caramelize). Pour and spread this caramel mixture into the bottom of a buttered 9-inch round baking pan. Arrange the mango slivers from Step 1 on top of the caramel in a decorative pattern, ensuring to fill all or most spaces for the best visual result. Set the pan aside.

Preheat the oven to 350°F (177°C). In a medium bowl, whisk together the all-purpose flour, baking powder, and salt, then set aside. In the bowl of an electric mixer fitted with the paddle attachment, beat the softened unsalted butter and white sugar at medium speed until the mixture is light and fluffy, about 5 minutes. Add the eggs, one at a time, followed by the egg yolk, beating well after each addition. Beat in the vanilla extract and plain yogurt until smooth.

Add half of the flour mixture from Step 3 to the wet ingredients in the mixer and beat at low speed just until combined. Mix in the mango juice concentrate or nectar, then add the remaining flour mixture and continue to mix until just combined. Be careful not to overmix the batter. I like to scrape down the bowl a couple of times to make sure everything is evenly combined.

Carefully spoon the batter from Step 4 over the arranged mango slivers in the cake pan, taking care not to disturb the design. Gently spread the batter evenly. Bake in the preheated oven for 33-37 minutes if using a dark pan, or 45-50 minutes if using a shiny pan, or until the cake is golden brown and a toothpick inserted in the center comes out clean. Let the cake cool on a wire rack for about 10 minutes.

Once the cake has cooled slightly, run a thin knife gently along the edge of the pan. Carefully invert the cake onto a platter and allow it to cool further. Serve the mango upside-down cake slightly warm or at room temperature. For a special touch, I sometimes serve it with a scoop of vanilla ice cream.