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Roll out dough and fit into a 9-inch pie pan.
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Put butter and brown sugar in a medium saucepan over medium-high heat. As the butter melts, stir to combine with the sugar. Once mixture is smoothly blended and beginning to bubble, cook for 2 minutes longer, whisking constantly.
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Remove from heat and add the cream, then whisk until smooth. Add the salt, vanilla, eggs, and cardamom, and whisk until evenly blended.
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Pour into the prepared pie shell. Bake for 30-35 minutes or until the filling quivers slightly when the pan is jiggled and the surface is puffy.
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Sprinkle surface of pie with sea salt and cool for at least one hour. Best served warm.