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1
In a medium saucepan, melt 4 tablespoons of the butter.
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2
Add the shallot and cook over moderate heat, stirring, until softened, about 2 minutes.
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3
Add the garlic, tomatoes, tomato paste and wine and bring to a boil.
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4
Simmer over moderately high heat, stirring, until nearly all the wine is absorbed and the tomatoes just start to pop, 4 to 5 minutes.
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5
Add the oats and chicken stock and cook over moderate heat, stirring occasionally, until the oats are just tender and suspended in a creamy sauce, 8 to 10 minutes.
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6
Stir in the 1/4 cup of basil, 1/4 cup of grated cheese and the remaining 1 tablespoon of butter.
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7
Season the oatmeal with salt and pepper and keep warm, adding tablespoons of water if it becomes too thick.
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8
Meanwhile, bring a large, deep skillet of water to a simmer over moderate heat.
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9
Add the white vinegar and a generous pinch of salt.
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10
Crack the eggs into a small bowl, one at a time, and carefully slide them into the simmering water.
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11
Poach the eggs over moderate heat until the whites are set but the yolks are still slightly runny, about 4 minutes.
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12
Transfer the poached eggs to paper towels to drain.
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13
Spoon the oatmeal into shallow bowls.
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14
Top with the poached eggs, garnish with basil and serve right away, passing additional cheese at the table.
