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1
Using 3 1/4-inch biscuit cutter or clean 6-ounce tuna can as template, cut ham slices into rounds.
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2
Whisk mayonnaise, 1 1/2 teaspoons Dijon mustard, orange juice, grated orange peel, and fresh lemon juice in small bowl to blend.
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3
(Ham and sauce can be prepared 1 day ahead.
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4
Cover separately and refrigerate.)
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5
Preheat oven to 300F.
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6
Fill large skillet with enough water to reach depth of 2 inches.
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7
Add white wine vinegar and 1 1/2 teaspoons salt to water.
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8
Bring to simmer over high heat.
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9
Reduce heat to medium-low.
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10
Spread 3 tablespoons butter and some additional Dijon mustard over split sides of English muffins.
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11
Melt remaining 1 tablespoon butter in heavy large skillet over medium-high heat.
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12
Add ham rounds and cook just until beginning to brown, about 1 minute per side.
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13
Place ham atop prepared English muffins.
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14
Arrange English muffins on baking sheet.
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15
Keep warm in oven while preparing eggs.
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16
Crack eggs into skillet of simmering water.
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17
Cook until whites are set and yolks are set to desired doneness, about 3 minutes for medium-set yolks.
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18
Using slotted spoon, transfer eggs to plate.
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19
Stir sauce in top of double boiler over simmering water until just heated through, about 2 minutes.
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20
Season sauce to taste with salt and pepper.
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21
Place 1 egg atop ham on each prepared muffin half.
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22
Spoon warm sauce over eggs, sprinkle with basil or parsley, and serve immediately.
