Trim the corn and cut off one end so that you can stand it upright. Using a sharp paring knife, moving from top to bottom, shave off the kernels. Place the kernels in a medium saucepan with enough water to barely cover, about 2 cups. Bring to a boil, covered, and reduce heat to simmer for for about 10 – 12 minutes, until the kernels are soft. Drain and reserve the corn cooking liquid.
Return the coarsely pureed kernels to the saucepan and add about 2/3 of the cooking liquid back in. Simmer over low heat for about 12 to 15 minutes, until the mixture thickens to the consistency of mashed potatoes and starts to sputter. If there is a lot of liquid left, continue simmering until most of it is cooked off. Stir in the butter, 3 tablespoons of olive oil, feta and salt and continue cooking over low heat, stirring with a whisk, until the polenta is thick and creamy.
In a medium frying pan over medium heat, warm 2 of the 4 tablespoons of olive oil and cook the onion until soft, about 8 minutes. Stir in the garlic. Add the tomatoes, raise the heat, and shuffle the frying pan over the heat vigorously to release the tomato juices a little without breaking them completely. Season with salt and set aside.
To serve: Spread the warm polenta onto serving plates or a platter. Add the green beans to the tomato mixture and shuffle back and forth over medium heat for a minutes, just to lightly warm through. Taste for salt and toss with oregano. Serve the green beans over the polenta and drizzle any remaining olive oil on top.