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1
Preheat the oven to 325F.
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2
Set a shallow 8-inch square or 11 x 7-inch baking dish inside 13 x 9-inch baking pan.
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3
Set a kettle of water on to heat.
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4
Heat a large skillet over medium heat; add the oil.
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5
When it is hot enough to sizzle a mushroom, add all of the mushrooms; cook, stirring, for 5 minutes.
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6
Add the onions cook over medium-low heat until the onions are tender and the mushrooms are golden brown, about 5 minutes.
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7
Meanwhile, finely chop the parsley, thyme, rosemary, and garlic together.
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8
Add to the mushrooms: cook for 1 minute.
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9
Stir in the roasted red peppers, 1 teaspoon salt, and a generous grinding of black pepper.
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10
Remove from the heat.
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11
Add the rice, breaking up any clumps with the side of a spoon; stir to blend.
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12
Let cool slightly.
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13
Gently stir in half of the goat cheese; transfer to the baking dish.
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14
Sprinkle the remaining goat cheese on top.
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15
Whisk the eggs and yolks in a large bowl until blended.
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16
Gradually whisk in the milk.
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17
Add 1 teaspoon salt and a grinding of black pepper.
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18
Carefully pour over the mushroom and rice mixture.
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19
Place on the center oven rack.
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20
Carefully add enough very hot water to the baking pan to come halfway up the sides of the baking dish.
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21
Bake until the custard is almost set in the center and the tip of a knife inserted just off center comes out clean, about 1 hour and 15 minutes.
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22
Let the pudding stand in the hot-water bath for 15 minutes before serving.
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23
(The center will continue cooking and setting as the pudding stands.)