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1
For the marinade: The day before you plan on cooking your steak, place the rib-eye in a resealable baggie along with the olive oil, rosemary, thyme and garlic.
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2
Move the herbs and garlic around in the bag to coat the steak with all the flavors.
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3
Refrigerate overnight.
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4
For the steak: Remove the steak from the refrigerator 30 minutes before cooking.
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5
Preheat the oven to 400 degrees F.
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6
Heat a grill pan over medium-high heat.
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7
Sprinkle the steak evenly with 1 teaspoon of the salt.
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8
Place the steak on the grill pan and sear for 5 minutes without moving the steak.
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9
Flip the steak and repeat on the other side.
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10
Remove the steak to a baking sheet and place in the oven for 10 minutes for medium doneness.
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11
Allow the steak to rest for 15 minutes.
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12
Meanwhile, in a small bowl mix together the lemon zest, lemon juice, 2 teaspoons olive oil, rosemary, thyme, 1/8 teaspoon of the salt and 1/8 teaspoon of the pepper.
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13
Set aside.
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14
Heat a small nonstick skillet over medium heat.
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15
Add 1 teaspoon olive oil and slide in the egg, being careful not to break the yolk.
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16
Sprinkle with the remaining 1/8 teaspoon salt and 1/8 teaspoon pepper.
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17
Reduce the heat to medium-low and gently cook the egg until the white is just set and the yolk is still soft, about 3 minutes.
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18
Transfer the rested steak to a serving plate.
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19
Scatter the arugula over the steak and drizzle 1 teaspoon of the herb oil.
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20
Lay the egg, sunny-side up, over the top.
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21
Drizzle with the remaining herb oil and season with a few grinds of black pepper.
