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1
Heat the oven to 350 degrees F and arrange a rack in the middle.
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2
Lightly flour a work surface and roll the dough out into a round approximately 12 inches in diameter and 1/4 inch thick.
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3
Line a 9-inch pie plate with the dough and trim off the excess.
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4
Pierce the bottom of the crust all over with a fork, line it with a piece of parchment paper or aluminum foil, and fill it with pie weights or dried beans.
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5
Bake until the crust starts to set, about 15 minutes.
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6
Remove the pie weights and parchment paper and continue to bake until the crust is dry and slightly brown, about 10 to 15 minutes more.
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7
Remove to a wire rack and set aside.
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8
Combine the vanilla seeds and pod (or vanilla extract, if using), milk, and cream in a small saucepan and bring to a simmer over medium-high heat.
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9
Remove from the heat.
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10
Meanwhile, melt the butter in a large saucepan over medium heat.
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11
Add 1/2 cup of the brown sugar, stir to combine, and cook, stirring often, until the mixture bubbles and there is a toasted smell (the butter should be brown but not burnt), about 5 minutes.
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12
Carefully whisk in the hot milk mixture and remove the saucepan from the heat to cool slightly, about 5 minutes.
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13
Remove and discard the vanilla pod.
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14
In a large bowl, whisk together the remaining 1/4 cup of brown sugar, egg yolks, and cornstarch until well blended and the whisk leaves a trail when lifted out of the mixture, about 3 minutes.
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15
Scrape down the sides of the bowl with a rubber spatula.
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16
While whisking constantly, slowly pour a third of the milk mixture into the egg yolk mixture and whisk until well combined.
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17
Add the egg mixture back to the remaining milk mixture and place the saucepan over medium-low heat.
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18
Cook, constantly scraping the bottom of the saucepan with a rubber spatula, until the mixture coats the back of a spoon, about 7 to 10 minutes; set aside.
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19
Pour the mixture into the pie crust and bake until the edges are set but the middle still jiggles slightly, about 25 to 30 minutes.
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20
Place the pie on a wire rack and let it cool completely, about 2 hours.
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21
Serve at room temperature or cold.
