In a saucepan, combine chopped rhubarb, sugar, cornstarch, and vanilla extract. Cook over medium heat until rhubarb is tender and mixture thickens, about 5-7 minutes.

Preheat the oven to 350°F (175°C). In a mixing bowl, cream together softened butter and sugar until light and fluffy.

Add eggs one at a time, mixing well after each addition. Stir in vanilla extract.

In another bowl, whisk together flour, baking powder, and salt. Gradually add to the butter mixture, alternating with milk, until just combined.

Pour half of the cake batter into a greased 9-inch round cake pan. Spread the rhubarb filling evenly over the batter, then top with the remaining batter.

Bake in the preheated oven for 30-40 minutes, or until a toothpick inserted into the center comes out clean.

Allow to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.