Bring 3 inches of water to a boil in a large wide pot. Heat the vegetable oil in a large nonstick skillet over high heat until very hot. Season the steak with salt and pepper, add to the skillet and cook until browned, 2 to 4 minutes per side for medium rare. Remove to a cutting board to rest.
Reduce the heat under the skillet to medium; add the spinach and 2 tablespoons water and cook, stirring occasionally, until wilted, about 2 minutes. Season with salt and pepper. Divide the English muffin halves among plates and top with the spinach.
Meanwhile, combine the egg yolk, butter, lemon juice and 1 tablespoon water in a small saucepan over medium heat. Cook, whisking, until the butter melts and the sauce thickens, about 3 minutes. Add the tarragon and season with salt and pepper. Cover and keep warm.
Add the vinegar to the boiling water, then reduce the heat to maintain a gentle simmer. Crack an egg into a small bowl or ramekin and carefully slide the egg into the water; repeat with the remaining eggs. Cook until the whites are set but the yolks are still jiggly, about 3 minutes. Remove the eggs with a slotted spoon, blot the bottoms dry on a kitchen towel and place on the English muffins.
Slice the steak against the grain and divide among the plates. Spoon the sauce over the eggs.
Tools You May Need
Photograph by Ryan Dausch
Tools You May Need
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