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1
Preheat the oven to 375F.
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2
Butter the bottom and sides of a 9-inch springform pan, and line the bottom with parchment paper.
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3
Close the latch, and place the pan on a large sheet of aluminum foil.
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4
Fold the foil up around the sides of the pan to prevent the filling from leaking out while the walnut wedge bakes.
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5
Place the pan on a baking sheet.
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6
Toast the chopped walnuts and walnut halves separately on a baking sheet, about 8 minutes, until theyve browned slightly and smell nutty.
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7
Place 3 tablespoons butter in a small saute pan.
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8
Split the vanilla bean lengthwise, and use a paring knife to scrape out the pulp and seeds onto the butter.
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9
To make sure not to lose any of the precious seeds, run your vanilla-coated knife through the butter.
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10
Add the vanilla pod to the pan, and cook the butter and vanilla over medium heat, swirling the pan a few times, until the butter browns and smells nutty.
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11
In a stand mixer fitted with the whisk attachment, beat the sugars, rum, and corn syrup at medium speed 4 to 5 minutes.
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12
Add the warm brown butter, and mix another 2 to 3 minutes to incorporate.
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13
Add the egg and yolk, and continue to mix at medium speed another minute or two.
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14
Spread the chopped walnuts in an even layer in the prepared pan.
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15
Place the walnut halves in concentric circles over the chopped walnuts.
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16
Pour the filling evenly over the nuts, and bake about 40 minutes, until the nuts are caramel-colored and the filling is set.
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17
Let cool about 30 minutes.
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18
Remove from the pan, and cut into wedges.
