01 - Preheat oven to 350°F. Grease an 8-inch round cake pan and line the bottom with parchment paper.
02 - In a medium bowl, sift together the flour, baking powder, and salt. Set aside.
03 - In a large bowl, beat the softened butter and sugar together using an electric mixer until pale and fluffy, about 3 minutes.
04 - Add the eggs one at a time, mixing thoroughly after each addition. Stir in the lemon zest and vanilla extract until evenly distributed.
05 - Fold in half of the flour mixture, followed by half of the milk. Repeat with the remaining flour and milk, mixing until just combined. Be careful not to overmix.
06 - Gently fold the diced rhubarb pieces into the batter using a spatula, distributing them evenly throughout.
07 - Spoon the batter into the prepared pan and smooth the top with a spatula. Bake for 50 to 55 minutes, or until a wooden skewer inserted into the center comes out clean.
08 - While the cake bakes, whisk together the lemon juice and sugar in a small bowl until the sugar has fully dissolved. Set aside.
09 - Remove the baked cake from the oven and immediately prick the surface all over with a skewer. Pour the lemon drizzle evenly over the hot cake, allowing it to seep into the holes.
10 - Let the cake cool in the pan for 15 minutes, then transfer to a wire rack to cool completely. Before serving, sprinkle with extra lemon zest or dust with powdered sugar if desired.