1. In a medium bowl, combine the salt and flour. Gradually whisk in the whole milk (a technique called building a slurry — adding liquid in stages to prevent lumps) until smooth. Set aside.
2. Beat the eggs in a separate bowl until thick and lemon-colored, 3 to 5 minutes by hand or 1 to 2 minutes with a hand mixer. The mixture should fall from the whisk in a pale, ribbon-like stream.
3. Add the beaten eggs to the flour-milk mixture and stir to combine.
4. Heat a 10-inch (25 cm) cast-iron skillet over medium heat until a drop of water skitters across the surface and evaporates immediately, about 2 minutes.
5. Add 2 tablespoons (30 g) of the butter to the pan. When the butter has melted and the foam begins to subside — but before it browns — pour in the egg mixture.
6. As the omelet sets on the bottom, lift the cooked edges with a wide spatula and tilt the pan so the uncooked egg runs underneath. Continue lifting and tilting around the perimeter until the top surface is barely wet and the underside is set and pale golden, 4 to 6 minutes total.
7. Add the remaining 1 tablespoon (15 g) butter in small pieces to any areas that are sticking or look dry.
8. Move the pan to a higher-heat burner or increase the heat to medium-high. Allow the omelet to brown on the bottom, 1 to 2 minutes, until the underside is deep golden and the omelet releases cleanly from the pan when you shake it gently.
9. Roll the omelet away from you using the spatula, then slide or invert it onto a warmed serving platter, seam side down. Serve immediately.
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