Preheat the oven to 375 degrees and grease 2 8-inch pie pans.
In a mixing bowl, whisk the eggs, milk, salt, and smoked paprika on medium speed until well-combined. I use my stand mixer rather than mixing by hand because it beats the eggs more evenly.
In a large skillet, heat the olive oil over medium heat and add the Swiss chard. Cover and saute for 2 or 3 minutes, until just beginning to wilt.
Divide the scallions, Swiss chard, and tomatoes evenly between the two pie pans. Pour the egg mixture over the vegetables, dividing it evenly between the two pans.
Bake for 25 to 30 minutes, until the eggs are set.
Let the quiche sit for at least 10 minutes before cutting. Serve warm or at room temperature.