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1
Preheat broiler.
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2
Line large baking sheet with foil.
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3
Remove and discard mushroom stems.
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4
Scoop out and discard tough inside centers where mushroom stems were attached.
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5
Brush both sides of mushrooms generously with olive oil.
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6
Place mushrooms, dark gill side up, on prepared baking sheet.
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7
Sprinkle mushrooms with minced garlic, then sprinkle generously with salt and pepper.
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8
Broil mushrooms about 5 inches from heat source until beginning to soften, about 5 minutes.
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9
Turn mushrooms over; broil until tender when pierced with knife, about 7 minutes longer.
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10
(Can be made 2 hours ahead.
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11
Let stand at room temperature.
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12
Before continuing, rewarm in 350F oven until heated through, about 10 minutes.)
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13
Whisk eggs, 2 tablespoons grated Parmesan cheese, chopped rosemary, salt, and pepper in large bowl to blend.
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14
Melt 5 tablespoons butter in heavy large skillet over medium-low heat.
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15
Add eggs to skillet and stir gently in circular motion with wooden spoon or heat-resistant rubber spatula, releasing cooked eggs from bottom of skillet and allowing uncooked portion of eggs to flow underneath.
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16
Cook until eggs are set but still soft, about 4 minutes total.
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17
Dot with remaining 1 tablespoon butter.
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18
Arrange hot portobello mushrooms, gill side up, on plates.
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19
Top with eggs, dividing equally.
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20
Sprinkle with remaining 2 tablespoons grated Parmesan cheese, dividing equally, and serve.