Heat a medium-size saute pan over medium-high heat and add 1 tablespoon butter and 1 tablespoon olive oil. Once the butter foams, saute scallions until soft and season with salt and pepper. Let cool slightly.
Add eggs, milk, and Parmesan cheese to a large bowl and whisk well to combine. Add the sauteed scallions and blend.
Heat a 14-inch nonstick pan over medium heat, add the remaining 1 tablespoon butter to melt. Once hot and foaming, add the egg mixture, do not stir, and turn heat to medium-low. Cover the pan and continue to cook for 12 to 15 minutes, until firm.