Preheat and Prep: Preheat your oven to 350°F and grease a 9x13-inch baking dish. Line the bottom with parchment paper for easy removal.
Combine Dry Ingredients: In a medium bowl, whisk together flour, pumpkin pie spice, baking powder, baking soda, and salt. Set aside.
Beat Egg Yolks: In a large bowl, beat egg yolks with ¾ cup sugar until pale and thick, about 3 to 4 minutes. Stir in pumpkin purée, milk, and vanilla extract until combined.
Fold in Dry Mixture: Gently fold the dry ingredients into the pumpkin mixture until just combined, taking care not to overmix.
Whip Egg Whites: In a separate clean bowl, beat egg whites on high speed until stiff peaks form, about 4 to 5 minutes. Add remaining ¼ cup sugar gradually while beating.
Fold Together: Carefully fold the beaten egg whites into the pumpkin batter in two additions, maintaining as much airiness as possible.
Bake: Pour batter into the prepared dish and bake for 25 to 30 minutes, until a toothpick inserted in the center comes out clean. The cake should be golden and spring back when lightly touched.
Combine Milks: In a medium bowl, whisk together evaporated milk, sweetened condensed milk, milk (or half-and-half), vanilla extract, pumpkin pie spice, and salt until smooth and well blended.
Cool and Pour: Let the mixture cool to room temperature, then pierce the warm cake all over with a fork or wooden skewer. Pour the tres leches mixture evenly across the entire surface, allowing it to absorb completely, about 5 to 10 minutes.
Chill: Cover with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, so the cake fully saturates and flavors deepen.
Chill Bowl and Beaters: Place a metal bowl and beaters in the freezer for 10 to 15 minutes to ensure the heaviest whipped cream possible.
Whip the Cream: Pour cold heavy cream into the chilled bowl and beat on medium-high speed until soft peaks begin to form, about 1 to 2 minutes. Add sifted confectioners' sugar and vanilla extract, then continue beating until stiff peaks form.
Spread Topping: Spread or dollop the whipped cream evenly over the chilled cake, or pipe it decoratively if desired.
Garnish: Dust the top with ground cinnamon for a warm, spiced finish that echoes the pumpkin theme.