In a medium skillet, heat dry milk powder over medium heat, stirring frequently with a small spatula, until milk solids are light golden brown; remove from heat, and stir, scraping bottom of skillet, until milk solids are deep golden brown. (The entire process should take 5 to 7 minutes.) Strain through a fine-mesh sieve into a heatproof bowl, and let cool completely.
Preheat oven to 350°F (180°C).
In the bowl of a stand mixer fitted with the whisk attachment, beat egg yolks and ½ cup (100 grams) sugar at medium-high speed until fluffy and pale yellow in color, 1 to 2 minutes, stopping to scrape sides of bowl. Add ½ cup (120 grams) whole milk, and beat at medium-low speed just until combined, stopping to scrape sides of bowl.
In a medium bowl, whisk together flour, ½ cup (48 grams) toasted milk powder, baking powder, and ¾ teaspoon salt. Fold flour mixture into egg yolk mixture until combined. (Mixture will be thick.) Transfer to a large bowl.
Clean bowl of stand mixer and whisk attachment. Using the whisk attachment, beat egg whites and cream of tartar at medium-high speed until foamy. With mixer on medium-high speed, add ½ cup (100 grams) sugar in a slow, steady stream, beating until stiff peaks form. (The entire process should take about 5 minutes.) Stir in one-fourth of egg white mixture until lightened and well combined; add remaining egg white mixture in three additions, folding until combined and no streaks or lumps remain after each addition. (Batter will start out thick but become lighter, smoother, and fluffier with each addition.) Pour batter into an ungreased 9-inch square ceramic baking dish. Gently tap sides of pan to help settle batter.
Bake until a wooden pick inserted in center comes out clean and an instant-read thermometer inserted in center registers 205°F (96°C), 35 to 40 minutes. Let cool in pan for 10 minutes. (Cake will deflate slightly.) Carefully run a small offset spatula around sides of pan to release sides of cake. Using a wooden skewer, poke holes every ½ inch all over top of hot cake.
In another medium bowl, whisk together condensed milk, evaporated milk, remaining ¾ cup (180 grams) whole milk, remaining ½ cup (48 grams) toasted milk powder, and remaining ¼ teaspoon salt. Gradually pour and spread milk mixture all over top and sides of warm cake, letting some milk mixture soak in between additions. Loosely cover cake, and refrigerate until chilled, at least 3 hours, or up to overnight.
When ready to serve, dollop Vanilla Whipped Cream on top of cake, and spread and swirl as desired. Garnish with toasted milk powder, if desired.