In a saucepan, whisk together brown sugar, white sugar, cornstarch, salt, and cardamom. Gradually whisk in the egg yolks and coconut milk until smooth.

Place over medium-low heat and cook, whisking constantly, until steaming, about 5 minutes. Raise heat to medium and continue whisking until the mixture thickens, about 5 minutes. When the custard begins to bubble, cook for 2 additional minutes to neutralize the egg yolks.

Remove from heat and stir in vanilla extract and shredded coconut.

Pour into the prepared pie crust and let cool at room temperature until a skin forms, about 30 minutes. Cover with plastic wrap and refrigerate for at least 4 hours or up to 24 hours.

Preheat the oven to 375°F. Spread the prepared Marshmallow Meringue evenly over the chilled custard, making sure it touches the edges of the crust.

Sculpt peaks and swirls in the meringue using the back of a spoon or a spatula.

Bake until the meringue is lightly browned, about 20 minutes. Let the pie cool at room temperature for 1 hour, then refrigerate until fully chilled, about 4 hours.