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First, we'll brown the butter. Melt the butter in a small stainless steel saucepan over medium heat, stirring regularly until melted. Continue cooking the butter until it turns golden and smells toasty. Immediately remove it from heat, transfer to a heat proof bowl (glass or metal), and set it aside.
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Preheat oven to 350. Mix together the dry ingredients (except the sugar) in a bowl and set it aside.
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In the bowl of a stand mixer fitted with the whisk attachment, beat the egg whites with the sugar at medium high speed until soft peaks form, set aside.
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In the bowl of an electric mixer fitted with the paddle attachment mixing at low speed, add the egg yolks to the chestnut spread, one at a time, mixing well after each addition. Add the brown butter and vanilla extract and mix until combined. Then alternate between adding the milk and flour mixture in 4 increments, mixing at low speed *just* until combined. Fold in the whipped egg white mixture until incorporated.
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I used the NordicWare Heritage Bundtlette pan that has a 4 cup capacity for 6 mini-bundts, and this recipe made 9 mini bundts. So you could use a 6 to 8-cup capacity bundt pan for one single bundt cake, or you could use the Bundtlette pan and clean it between uses.
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Spoon the mixture into the mini bundt pan sprayed with cooking oil and sprinkled with almond flour, filling the bundts about 4/5ths full.
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Bake at 350 until a toothpick inserted into the mini bundt comes out clean, about 25 to 30 minutes (if you're making one single large bundt cake, the cooking time will be longer).
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Remove the pan from the oven and allow to cool for 10 minutes before flipping onto a wire rack and unmolding the mini bundt cakes.
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Place unmolded cakes in large casserole dish lined with parchment paper. Drizzle with the syrup, allow them to soak in the syrup for 10 minutes, then remove and allow to cool + drain on a rick rack with a cookie sheet under it to catch the syrup drippings. Garnish with the chopped pistachios and serve.