Preheat the oven to 350°. Heat the oil in a 9-inch nonstick ovenproof skillet. Add the onion, season with salt and cook until softened, about 3 minutes. Add the fennel and marjoram and season with salt. Cook over low heat, stirring occasionally, until the fennel is softened, about 5 minutes. Season with pepper and transfer the sautéed vegetables to a plate.
In a medium bowl, whisk the eggs and season with salt and pepper. Melt the butter in the skillet and add the eggs. Spoon the vegetables evenly over the eggs and dot with the feta. Bake for about 12 minutes, or until the eggs are just set. Slide the frittata onto a large serving plate and sprinkle with the chopped basil. Let the frittata cool slightly, then cut into wedges and serve warm or at room temperature.
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