Preheat the oven to 350 degrees. In a medium mixing bowl, scramble the eggs. Add a splash of milk, if using, and season with sea salt and black pepper. Set aside.
In a medium nonstick skillet or cast iron pan, add the olive oil and turn the heat to medium. Add the scallions and chives and stir to coat. Cook for a minute or two and then add the tomatoes. Stir and continue cooking until the tomatoes start to break down, 2-3 minutes. Add 1 cup of chopped arugula, stir to coat. Pour in the eggs and sprinkle the feta across the top of the egg mixture.
Place the skillet into the oven and cook for 10-15 minutes, or until the center of the frittata has set. While it is cooking, place 2 cups of arugula in a mixing bowl with some thinly sliced shallot. Squeeze a little lemon juice and a drizzle of olive oil in the bowl. Season with sea salt and black pepper and toss to coat. Once the frittata is finished, remove it from the oven. Cut it into 6-8 wedges. Top with some arugula salad and serve.