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Step 1
Season each side of each steak with 1/4 teaspoon salt and 1/4 teaspoon pepper. Heat a large, heavy-bottomed skillet with a lid over medium-high heat. Melt 1 tablespoon of the butter with the oil, then add 2 of the steaks. Sear on each side for 2 minutes, then remove to a plate and repeat with the remaining 2 steaks; transfer to the plate.
Step 2
Reduce the heat under the skillet to medium, melt the remaining 2 tablespoons butter and add the onions. Season with 1/2 teaspoon salt and a few grinds of pepper. Cook until the onions are browned on the edges and starting to soften, about 5 minutes. Sprinkle the flour over the onions and stir to coat the onions. Cook until the flour starts to brown, another 30 seconds. Slowly pour 2 cups of water into the onion mixture, stirring constantly, until all the water is combined and creates a sauce. Bring to a simmer, then nestle all of the steaks back into the skillet, adding any juice that may have accumulated on the plate. Reduce the heat to low, cover and cook until the liquid starts to develop into a thickened sauce, about 10 minutes.
Step 3
Uncover, stir and continue to cook until the sauce thickens to a hearty gravy, another 2 to 3 minutes. Remove from the heat. Immediately serve the steaks covered in the onion gravy.