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1
Melt 1 tablespoon of the butter in an 8-inch nonstick frying pan over medium-high heat until foaming.
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2
Add the shallot and cook, stirring occasionally, until softened, about 2 minutes.
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3
Add the mushrooms and thyme, season with a pinch each of salt and pepper, and cook, stirring rarely, until the mushrooms are golden brown, about 4 to 5 minutes.
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4
Add the sherry and cook until evaporated, about 1 minute.
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5
Transfer to small heatproof bowl and set aside.
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6
Wipe out the frying pan with a paper towel; set the pan aside.
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7
Whisk the eggs, milk, and measured salt and pepper in a large bowl until pale yellow and the egg yolks and whites are evenly combined.
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8
Set 2 serving plates aside.
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9
Melt 1 tablespoon of the butter in the reserved frying pan over medium heat until foaming.
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10
Add half of the egg mixture (about 3/4 cup) to the pan and stir constantly with a rubber spatula, moving the eggs around until they form small curds, about 2 to 3 minutes.
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11
Gently shake the pan and use the spatula to spread the egg mixture evenly across the panthe top of the eggs should have a creamy consistency.
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12
Sprinkle with half of the cheese.
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13
Spread half of the mushroom mixture down the middle third of the egg mixture.
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14
Remove the pan from heat.
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15
Using the spatula, fold a third of the omelet over and onto itself, making sure to fold it over the filling.
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16
Gently push the folded side of the omelet toward the edge of the pan.
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17
Tilt the pan over one of the serving plates and roll the omelet onto the plate, seam side down.
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18
Repeat with the remaining tablespoon of butter, eggs, fontina, and mushroom filling.
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19
Serve immediately.
