Heat oven to 350℉. Butter an 8 or 9-inch round cake pan and line it with a circle of parchment. Pour in the cooked rhubarb, arrange evenly, and set aside.
In a small bowl, whisk together the flour, baking powder, and salt.
In a large bowl and using an electric mixer on medium speed, cream the butter, scraping down the sides of the bowl as necessary, until the butter is lighter in color, about 45 seconds. Then add the sugar in a steady stream and scrape down the bowl again. Continue to mix on medium speed until the mixture is very light in color and texture, about 4 to 5 minutes.
In a small bowl whisk the eggs. Slowly pour in the eggs a little at a time, and beat very well for about 2 minutes.
Combine the vanilla and milk in a small bowl or measuring cup.
With the mixer on low, add the flour mixture in two doses, alternating with the milk. Scrape down the sides of the bowl in between additions.
Pour the batter on top of the rhubarb, smoothing gently. Place cake in the oven and bake for 25 to 30 minutes, or until a toothpick inserted in the center comes out clean.
Remove from the oven and set on a rack to cool for 10 minutes. Run a butter knife around the side of the pan to loosen the cake, then turn out onto the rack to finish cooling completely.