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1
Prepare the grill or barbecue (medium-high heat).
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2
Sprinkle the steaks with salt and pepper and drizzle with the 3 tablespoons of olive oil.
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3
Grill to desired doneness, about 5 minutes per side for medium-rare.
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4
Transfer the steaks to a cutting board.
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5
Tent with foil and let stand 10 minutes.
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6
Meanwhile, melt 2 tablespoons of butter in a heavy large saucepan over medium-high heat.
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7
Add the onions and saute until tender, about 5 minutes.
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8
Season with salt.
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9
Add the garlic and oregano and saute until fragrant, about 30 seconds.
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10
Stir in the tomato paste and cook for 2 minutes, stirring constantly.
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11
Whisk in the wine.
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12
Simmer until the sauce reduces by half, stirring occasionally, about 10 minutes.
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13
Remove the skillet from the heat.
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14
Strain the sauce into a small bowl, pressing on the solids to extract as much liquid as possible.
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15
Discard the solids in the strainer and return the sauce to the saucepan and bring back to a slow simmer.
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16
Cut the remaining 4 tablespoons of butter into small 1/2-inch chunks and whisk in the sauce a little at a time.
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17
Season the sauce, to taste, with salt and pepper.
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18
Thinly slice the steaks across the grain.
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19
Divide the steak slices among 6 plates.
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20
Drizzle the sauce over the steak, drizzle a little more extra-virgin olive oil and serve.
