Preheat oven to 325F / 170C. Lightly grease a donut pan with oil.
Add the spinach to a pan and heat until wilted. Run under cold water to refresh, drain and squeeze out excess moisture. Add the spinach and milk to a tall container and puree well with a hand held stick blender.
Zest and juice the lemon, then set aside. They will be used for both the batter and glaze.
In a large bowl, beat the spinach puree, 1 teaspoon of zest, 1 tablespoon of lemon juice, sugar, cooled melted butter, egg and vanilla together. Sift in the flour and baking powder and gently combine.
Fill the doughnut molds with the batter until nearly full and bake for 15 minutes or until springy and an inserted skewer comes out clean. Allow to cool in the tray for 5 minutes, then carefully remove from the pan to cool completely on a wire rack.
For the glaze,
Mix the powdered sugar with 1 ½ tablespoon of the lemon juice. Add more juice (or water), sparingly, if needed to achieve a thick but pourable consistency. Drizzle over the completely cooled doughnuts and sprinkle with a little zest.