Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a medium-sized bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the butter mixture, alternating with the clementine juice and milk. Begin and end with the dry ingredients. Mix until just combined.
Fold in the clementine zest, ensuring it's evenly distributed throughout the batter.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for approximately 35-40 minutes, or until a toothpick inserted into the center comes out clean.
While the cake is cooling, prepare the vanilla glaze. In a small bowl, whisk together powdered sugar, clementine juice, and vanilla extract until smooth and pourable. Adjust the consistency by adding more juice or powdered sugar as needed.
Once the cake has cooled completely, drizzle the vanilla glaze over the top, allowing it to drip down the sides.
Slice, serve, and enjoy!