Preheat oven to 325°; brush the inside of a 10-cup Bundt pan thoroughly with melted butter and dust it lightly with flour (use a pastry brush to help distribute the flour and tap out any excess).
Whisk the flour, baking powder, and salt in a bowl until well combined.
In the bowl of a stand mixer fitted with paddle attachment, beat the butter with the sugar on medium speed for 2-3 minutes, until light and fluffy.
In a medium bowl, whisk the egg yolks until they are light and lemon-colored, then add them to the butter-sugar mixture and beat until just blended.
With the mixer on low, add the flour mixture (in three increments) alternating with the milk (in two increments), beginning and ending with flour and beating until thoroughly incorporated after each addition.
Add the vanilla, lemon zest, and lemon juice; beat 2 minutes.
Pour batter into prepared pan, smooth the top; bake for 1 hour, until a cake tester comes out clean.
Let the cake cool for about 15 minutes in the pan on a wire rack, then invert the cake onto the rack and let it cool completely.
Make the icing-combine the powdered sugar with the butter, lemon zest, lemon juice, and cream in a small bowl; stir vigorously until the mixture is smooth, thick, and pourable.
Add more cream in needed to obtain the desired consistency.
Pour the icing over the cooled cake and serve.
The cake will keep in an airtight container at room temperature for up to 2 days.
The uniced cake will keep, wrapped well in a layer of plastic wrap and a layer of foil, in the freezer, for up to 2 weeks.