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1
Make basil oil: Place basil and olive oil in a blender and puree.
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2
Put mixture in a saucepan and bring to a boil over moderate heat, simmer 45 seconds.
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3
Strain through a fine-mesh strainer.
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4
Immediately strain oil again through a flat bottomed paper filter, such as those used for drip coffee machines (acone shaped filter will get clogged).
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5
You may need to gently squeeze the filter to force the oil out.
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6
Let filtered oil settle for a few hours, then pour off any clear oil, leaving the dark behind.
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7
Pour through a funnel into a bottle for storage.
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8
Cover and refrigerate.
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9
Use within 1 month.
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10
Preheat a broiler or a lightly oiled stove-top grill pan.
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11
Bring the water to a boil in a medium saucepan.
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12
Salt the water, add the vinegar, and then lower the heat so the water barely bubbles.
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13
One at a time, break the eggs into a custard cup or small bowl, and then pour into the water, trying not to break the yolks.
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14
With a slotted spoon, gently lift and shape the whites around the egg yolks until glazed but still liquid, about 2 1/2 minutes longer.
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15
While the eggs poach, toast the bread slices on both sides.
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16
Put a slice of toast on each of 2 plates.
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17
Immediately top with the prosciutto so that it softens from the heat of the toast.
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18
Lift the poached eggs out of the water with a slotted spoon, letting excess water drip off, and then place an egg on each toast.
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19
Drizzle each toast with 2 teaspoons basil oil and then grind a little black pepper over each.
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20
Serve immediately.
