Preheat the oven to 350. Lightly butter a 9-by-13 inch glass or ceramic baking dish. In a medium bowl, whisk the flour with the baking powder and salt. In the bowl of a stand mixer fitted with the paddle, beat the eggs with the sugar and 1 teaspoon of vanilla at medium-high speed until very light and fluffy, about 10 minutes. Add half of the flour mixture and mix at low speed until just incorporated. Gradually add the whole milk, then mix in the remaining flour mixture.
Pour the batter into the prepared baking dish and bake for 25 minutes, or until center of the cake springs back to the touch. Transfer the baking dish to a rack and let the cake cool for at least 30 minutes.
Meanwhile, in a medium saucepan, whisk the cream with the evaporated milk, cinnamon stick and cloves and bring to a boil over moderately high heat. Reduce the heat and simmer 3 minutes. Remove from the hear, cover and let steep for 10 minutes.
In a heatproof bowl, combine the condensed milk with the remaining 1 teaspoon vanilla and the ground cinnamon. Strain the steeped cream mixture into the condensed milk and stir to combine. Let cool for 20 minutes.
Using a fork, poke holes all over the cooled cake. Gradually pour the milk mixture over the entire cake. Cover with plastic wrap and refrigerate for at least 4 hours or overnight.