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1
Preheat oven to 400F.
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2
Toss tomatoes and mushrooms with salt, pepper, and 2 tablespoons oil in a roasting pan.
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3
Arrange tomatoes cut sides up, then bake vegetables in lower third of oven until softened, about 20 minutes for mushrooms and 30 minutes for tomatoes.
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4
(Transfer mushrooms to a bowl while tomatoes finish roasting.)
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5
Transfer 8 tomato halves to a blender and puree with 1 tablespoon oil until smooth.
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6
(Thin sauce with water if desired.)
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7
Season with salt and pepper and transfer to a small ovenproof dish for reheating.
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8
Brush both sides of bread slices with remaining 2 tablespoons oil, then bake on a baking sheet in upper third of oven until crisp and golden on edges, about 10 minutes.
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9
Rub tops of toasts with cut sides of garlic.
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10
Leave toasts on baking sheet.
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11
(Leave oven on.)
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12
Fill a deep 12-inch skillet or small flameproof roasting pan with 1 1/4 inches cold water.
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13
Add vinegar and bring to a simmer to poach eggs.
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14
Reheat tomato sauce and roasted tomatoes and mushrooms in lower third of oven 5 to 10 minutes.
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15
Meanwhile, fold a slice of ham on top of each toast and heat in upper third of oven until warm, about 3 minutes.
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16
While other ingredients are reheating, break 1 egg into a cup, then slide egg into simmering water.
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17
Repeat with remaining eggs, spacing them apart, and poach at a bare simmer until whites are firm but yolks are still runny, 2 to 3 minutes.
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18
Transfer eggs with a slotted spoon to paper towels to drain and season with salt and pepper.
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19
Put 1 or 2 toasts on each plate and top each with a tomato half and a poached egg.
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20
Drizzle with tomato sauce and scatter mushrooms around eggs.
