Beat the eggs, oil, vanilla and sugar until well blended. Fold in the zucchini.
Whisk the flour, salt, baking powder, and baking soda to combine. Slowly add it to the wet mixture, mixing just enough to blend.
Fold in the blueberries, and pour the batter into the prepared pan. Bake for about 50 minutes, just until the top is turning golden and a toothpick inserted in the center comes out without wet batter clinging to it. Cool on a rack.
To make the frosting, put the softened butter into the bowl of a food processor and process until creamy. Add the sifted powdered sugar, one cup at a time, processing till smooth after each addition. After the second cup of sugar add in the lemon juice. Scrape down the sides of the machine as necessary. Adjust the texture by adding a little more lemon or a little more sugar.
Frost the cooled cake and store in the refrigerator.
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Notes
Reader Lillia reports in the comments below that this cake can easily be made gluten free using King Arthur's Measure for Measure Gluten Free Flour.
I felt that this blueberry zucchini snack cake was at its best chilled, so I kept ours in the refrigerator. The frosting is butter-rich, so especially in warm weather this makes sense, and the texture of the chilled frosting is out of this world.
For all your chocoholics out there, you really need to check out my Cold Chocolate Snacking Cake ~ it's meant to be eaten straight from the fridge, and I guarantee you won't be able to control yourself around it