In a small bowl or measuring cup combine ½ cup whole milk with 2 tablespoons white vinegar — stir briefly and allow to sit for 3–5 minutes until milk curdles slightly and thickens — this creates a quick homemade buttermilk.
In a large mixing bowl combine 4 tablespoons melted cooled butter, granulated white sugar, and vanilla extract — mix well until combined.
Add the prepared buttermilk mixture to the butter and sugar and stir to combine.
Add all-purpose flour, baking powder, and pinch of baking soda to the wet mixture — mix until a smooth batter forms — should not be too thick or too thin similar to slightly thick pancake batter — do not overmix once flour is added.
Line a 9x9 inch square baking pan or similar-sized pan with parchment paper and pour batter in — spread evenly.
Cook on stovetop over medium flame in a covered pan for 20–25 minutes OR bake in preheated oven at 350°F for 20–25 minutes until cake is set golden and a toothpick inserted in center comes out clean.
Allow cake to cool completely before proceeding — adding soaking liquid to a warm cake causes it to fall apart rather than absorb cleanly — do not rush this step.
While cake cools make the mango three-milk soaking mixture — place fresh mango pulp in a blender with 1½ cups whole milk and blend until completely smooth and uniform with no fibrous pieces remaining.
Pour mango milk into a large bowl and add heavy cream and sweetened condensed milk — stir everything together until completely combined into a rich sweet tropical three-milk mixture — taste and confirm it is sweet creamy and deeply mango-flavored.
Once cake is completely cool demold from pan.
Pour a generous layer of mango milk mixture into the bottom of a deep serving dish — enough to create a visible pool at the base.
Place cooled cake on top of the mango milk pool.
Use a fork skewer or toothpick to poke many holes all over the entire surface of the cake — the more holes the more thoroughly the soaking liquid penetrates the crumb.
Spoon additional mango milk mixture slowly and generously over the entire surface of the cake — add in stages allowing each addition to absorb before adding the next — goal is for every part of the cake to be completely saturated wet throughout.
Place a large bowl in the freezer for 5 minutes to chill thoroughly.
Pour cold heavy whipping cream into the chilled bowl and whip using hand mixer stand mixer or vigorous hand whisking on high speed until stiff peaks form — cream should hold its shape firmly when beaters are lifted — do not over-whip.
Spread whipped cream generously and evenly over the entire top surface of the soaked cake.
Arrange fresh mango pieces over the whipped cream surface in a decorative pattern.
Scatter roughly chopped pistachios over the mango pieces for contrasting color and nutty crunch.
Place assembled cake in the freezer for exactly 1 hour — this allows all layers to set the soaking milk to distribute evenly and whipped cream to firm up for clean slicing.
Remove from freezer allow to sit at room temperature for 5 minutes then slice into squares or rectangles and serve immediately.