Heat oven to 350°F. Grease a 9" x 13" baking dish; set aside.
In the bowl of a stand mixer fitted with paddle attachment, beat eggs and sugar on medium-high for 10 minutes until fluffy and pale yellow.
While eggs/sugar are whipping, sift flour, baking powder, and salt together in a medium bowl.
After 10 minutes of whipping, reduce mixer speed to low. Add half of flour mixture 1–2 tablespoons at a time. Slowly pour in milk. Then add remaining half of flour mixture 1–2 tablespoons at a time.
Briefly and gently mix batter with a silicone spatula, making sure to incorporate all sneaky, hidden pockets of flour.
Pour batter into prepared pan, smoothing top with an offset spatula or the back of a spoon.
Bake for 25 minutes. Cake is done when a wooden pick inserted in the centre comes out clean with only a few fluffy crumbs attached. When done, the cake should also spring back when gently touched.
While cake is baking, make milk tea cream. In a small pot over medium heat, warm cream, stirring occasionally. When a few bubbles appear, remove from heat and whisk in milk tea powder. Steep for 10 minutes.
Set a fine-mesh sieve over a large, heatproof bowl with a spout. Pour steeped cream through sieve. Discard milk tea blend.
Whisk evaporated milk and condensed milk into steeped cream. Set aside.
When cake is done, place baking dish on wire rack. Allow to cool for 30 minutes.
Using a skewer or cake tester, poke A LOT of holes in the cake. You basically want to poke as many holes as you can without destroying the cake.
If necessary, gently run a knife around the edges of the cake to unstick the sides from the pan.
Slowly pour three-milk syrup over warm cake, pausing as necessary to give the cake time to absorb the liquid. This step will take a little while, as you need to make sure that the cake properly and fully absorbs the liquid. NOTE: Don’t neglect the edges! You want all parts of the cake to get some of the three-milk syrup.
After all of the three-milk syrup has been absorbed, cover baking dish with cling film. Refrigerate for at least 6 hours or overnight.
When you’re ready to continue, place metal mixing bowl and whisk attachment in freezer for at least 15 minutes.
In the chilly bowl of a stand mixer fitted with cold whisk attachment, whip heavy cream, sour cream, vanilla, and salt until stiff peaks form.
Retrieve cake from fridge. Using an offset spatula, evenly spread whipped cream over cake. Place dish in fridge for 15–30 minutes.
Retrieve cake from fridge. Scatter brown sugar boba on top.