On a lightly floured surface, roll Pâte Brisée into a 12-inch circle (about 1⁄8 inch thick). Transfer to a 9-inch deep-dish pie plate, pressing into bottom and up sides of plate. Trim excess dough to 1⁄2 inch beyond edge of plate. Fold edges under, and crimp as desired. Dock bottom of dough with a fork. Freeze until firm, about 15 minutes.
Preheat oven to 425°F (220°C).
Top dough with a piece of parchment paper, letting ends extend over edge of plate. Add pie weights.
Bake until edges are golden brown, about 15 minutes. Carefully remove parchment and weights, and bake until bottom is golden brown and dry, 5 to 7 minutes more. Let cool completely.
In the bowl of a stand mixer fitted with the paddle attachment, beat cream cheese at medium speed until creamy, about 3 minutes. Add condensed milk and coconut milk, beating until smooth and stopping to scrape paddle and bottom and sides of bowl. Transfer cream cheese mixture to a large bowl.
In same bowl of a stand mixer fitted with the whisk attachment, beat 3⁄4 cup (180 grams) cold cream and coconut extract at medium-high speed until stiff peaks form, 3 to 4 minutes. Whisk one-third of whipped cream mixture into cream cheese mixture until smooth. Whisk in remaining whipped cream mixture.
Divide cream mixture in half. Fold melted chocolate into one portion, and spread into bottom of cooled prepared crust.
Fold flaked coconut into remaining cream mixture, and gently spread onto chocolate layer. Loosely cover and refrigerate until set, at least 4 hours, or up to overnight.
Just before serving, beat remaining 1¼ cups (300 grams) cold cream at medium-high speed until medium peaks form, 2 to 3 minutes. Spread onto pie; garnish with toasted coconut, if desired. Refrigerate in an airtight container for up to 3 days.