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1
Heat the oven to 350 degrees F and arrange a rack in the middle.
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2
Generously coat the wells of a 12-well muffin pan with butter; set aside.
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3
Heat 1 tablespoon of the oil and the measured butter in a medium frying pan over medium heat until the oil is shimmering and the butter has melted.
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4
Add the diced onion and cook, stirring rarely, until it is a deep golden brown, adjusting the heat as necessary if it starts to brown too much, about 30 minutes.
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5
Season well with salt and pepper, add the thyme, and stir to combine.
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6
Transfer the mixture to a medium bowl.
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7
Meanwhile, clean, trim, and slice the mushrooms 1/2 inch thick; set aside.
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8
Crumble the goat cheese into pea-sized pieces and set aside.
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9
Return the frying pan to medium heat, add the remaining tablespoon of oil, and heat until shimmering.
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10
Add the sliced mushrooms, season with salt and pepper, and cook, stirring rarely, until golden brown, about 10 minutes.
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11
Add to the bowl with the onion.
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12
Add the goat cheese to the bowl and stir to evenly combine; set aside.
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13
Place the eggs and milk in a large bowl and whisk until the eggs are broken up and evenly combined with the milk, about 1 minute.
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14
Add the measured salt and whisk to combine.
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15
Divide the onion-mushroom-cheese mixture evenly among the wells of the prepared muffin pan.
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16
Fill each well almost to the top with the egg mixture.
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17
Bake until each frittata is puffed and the center is just set, about 12 to 15 minutes.
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18
Remove the pan to a wire rack until its cool enough to handle, about 5 minutes (the frittatas will deflate).
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19
Run a small knife around the perimeter of each well to loosen and remove the frittatas.
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20
Serve warm or at room temperature.
