Candied Walnut Wedge

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