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1
In a medium light-colored skillet, melt 16 tablespoons (2 sticks) of the butter over medium-high heat.
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2
Cook, swirling the pan occasionally, until the milk solids are golden brown and the butter smells nutty, 4 to 6 minutes.
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3
Immediately transfer the butter to a large bowl (this will be for the cake batter); be sure to scrape out the browned bits from the bottom of the skillet.
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4
Wipe the skillet out and repeat the same process with the remaining 3 tablespoons butter.
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5
Transfer the butter to a medium bowl (this will be for the glaze).
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6
Set both bowls aside until the butter has solidified to the texture of softened butter.
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7
Preheat the oven to 350 degrees F. Butter a 4 1/2- by 8 1/2-inch loaf pan.
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8
To prepare the cake, whisk together the flour, baking powder and salt in a medium bowl and set aside.
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9
Add the granulated sugar to the 2 sticks of browned butter and beat the mixture with an electric mixer on medium-high speed until light and fluffy, 3 to 4 minutes.
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10
Add the eggs one at a time, beating after each addition.
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11
Then add the vanilla bean seeds.
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12
Beat in the flour mixture just until combined.
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13
Transfer the batter to the prepared pan.
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14
Bake until the cake is golden brown and a toothpick inserted in the center comes out with moist crumbs attached, 60 to 70 minutes.
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15
Transfer the cake to a rack to cool for 20 minutes, then remove the cake from the pan and let cool completely.
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16
Add the cream cheese to the 3 tablespoons browned butter and beat with an electric mixer on medium until fluffy.
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17
Beat in the confectioners' sugar.
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18
Add enough milk to the mixture to make a thick but pourable glaze.
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19
Top the cooled cake with the glaze before slicing.
