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1
Sauce
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2
Boil cream in heavy medium saucepan over medium-high heat until reduced to 1 cup, watching closely and adjusting heat to prevent cream from boiling over, about 12 min. Whisk in lemon juice and mustard. Season with salt and pepper to taste. Cover and chill
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3
Eggs
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4
Bring large nonstick skillet of water to simmer over medium heat. Add vinegar. Crack 1 egg into a small custard cup and carefully transfer to water, submerging cup to allow egg to slip into water. Repeat with 3 more eggs. Poach eggs until whites are set and yolks are still runny, about 3 min. Using slotted spoon, transfer eggs to a bowl of ice water. Repeat with remaining 4 eggs. Cover and chill.
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5
Hash
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6
Place potatoes in medium saucepan. Add enough cold water to cover by 1 inch. Bring to boil; reduce heat to medium and simmer until potatoes are tender, about 12 min. Drain. When cool enough to touch, peel potatoes. Press potatoes through a ricer, or mash finely with a potato masher.
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7
Heat 2 tsp EVOO in heavy medium skillet over medium-high heat. Add fennel, peppers (both) and onion. Saute until soft, about 5 min. Add to potatoes. Add crab, thyme, and tarragon; toss to distribute evenly, breaking up large crab pieces. Form crab mixture into eight 1in high cakes. Place on rimmed baking sheet. (can be made 8hrs ahead) Cover and chill.
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8
Heat 1 tblsp EVOO in large pot over medium-high heat. Add shallots and garlic and stir until soft, about 1 min. Add spinach. Cook until wilted, stirring often, about 3 min. Keep warm.
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9
Melt butter with remaining 2 tblsp EVOO in another large heavy skillet. Pry crab hash cakes until browned and crisp, 3-4 min per side. Transfer 2 cakes to each of the 4 plates. Top with spinach mixture. Warm eggs in lightly simmering skillet of water for about 1 min. Using slotted spoon, transfer WELL DRAINED eggs atop spinach mixture.
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10
Rewarm sauce, spoon over eggs and serve.