Preheat the oven to 350°F (180°C) and butter and line with parchment a 9-inch (23cm) round cake pan.

Zest the oranges and place the zest in the bowl of a food processor. Cut away all of the white pith and discard along with any seeds from the flesh. Place the flesh in the food processor. Process the oranges until finely ground.

To the bowl of the food processor, add the butter, sugar, and eggs and process until well combined, scraping down the sides of the bowl once or twice.

In a medium mixing bowl, whisk together the flour, baking powder, and salt, and then pour the orange mixture into the flour. Process together until the batter is just combined.

Spread the batter evenly into the prepared cake pan and bake for 45-50 minutes, until a wooden skewer inserted into the center comes out clean. Let cool for 10 minutes before releasing the sides of the pan to let cool completely.

Once the cake is cooled, make the glaze: combine the powdered sugar, 1 tablespoon of milk, and vanilla extract. If the glaze is too thick, add the other tablespoon of milk. Drizzle over the cake. Let set before serving.

Serve with some whipped cream. Store leftovers in an airtight container at room temperature for up to 3 days.