Preheat the oven to 350°F (175°C). Lightly butter the sides of a 9-inch cake pan with at least 2-inch tall sides.
Prepare the cherry topping: Place the cake pan directly on the stovetop over low heat. Add 4 tablespoons of unsalted butter and melt it completely. Stir in ¾ cup of packed light brown sugar until fully combined and smooth. Remove the pan from heat and evenly spread the mixture across the bottom.
Arrange the cherries: Place the halved cherries cut-side down over the sugar-butter layer, covering the bottom of the pan in a single layer. Press them down gently to help them stick.
Mix the dry ingredients: In a medium bowl, whisk together 1½ cups of all-purpose flour, 2 teaspoons of baking powder, and ¼ teaspoon of salt. Set aside.
Make the batter base: In a large bowl, use a hand mixer to beat 1 cup of granulated sugar and 8 tablespoons (½ cup) of softened butter on high speed for about 5 minutes, until the mixture is light and fluffy.
Add egg yolks and vanilla: Beat in 2 egg yolks, one at a time, mixing well after each addition. Then add 1 teaspoon of vanilla extract and mix to combine.
Incorporate milk and dry ingredients: Add ½ cup of lukewarm whole milk and mix on medium-low speed until well blended. Gradually add the dry flour mixture and continue mixing on low speed just until combined.
Beat egg whites: In a separate clean bowl, beat 2 egg whites with ¼ teaspoon of cream of tartar until stiff peaks form (stiff but not dry).
Fold egg whites into batter: Gently fold the whipped egg whites into the cake batter in two additions, folding just until no streaks remain. Be careful not to deflate the mixture.
Assemble and bake: Pour the batter over the cherries in the cake pan and smooth the top with a spatula. Bake in the center of the oven for 55 minutes, or until a toothpick inserted into the center comes out clean and the top is golden.
Cool and invert: Allow the cake to cool in the pan for 10 minutes. Run a dull knife around the edges to loosen it. Place a serving platter over the cake pan and carefully invert the cake onto the platter. Let it rest for 5 minutes before lifting off the pan.
Serve: Serve warm or at room temperature. Enjoy as is, or with whipped cream or vanilla ice cream.