Preheat the oven to 350˚F. Generously butter a 10-cup capacity Bundt pan and set aside.
In a large bowl, combine eggs and zest of both lemons. Beat with a hand mixer on medium speed for about 2 minutes, or until the eggs start to foam and turn light yellow.
Add the sugar and continue mixing at medium speed for about 2 minutes more, or until sugar has dissolved.
Set a fine mesh strainer over the bowl and sift the flour in to remove any clumps. Mix briefly at medium speed until combined, about 1 to 2 minutes. Add milk, oil and vanilla extract and mix until combined.
In a small bowl, add the juice of two lemons, then stir in baking powder. It should bubble up exuberantly, just like you are!
Add the baking powder and lemon mixture to the bowl and mix one more time to fully incorporate, about 1 to 2 minutes.
Scrape the batter into the prepared pan and bake for about 65 to 75 minutes, or until a cake tester inserted in the center comes out clean.
Let cool for at least 20 minutes in the pan, then invert onto a wire rack to cool fully.
Once cool, set on a cake plate or platter and dust with powdered sugar before serving.