Preheat oven to 350°F. Grease 2 (8-inch) round cake pans with butter. Line bottoms of pans with parchment paper; line sides with 2 (26- x 2-inch) parchment paper strips.

Process pandan leaves and ½ cup water in a food processor until mixture forms a finely chopped pulp, 3 to 4 minutes, stopping to scrape down sides of processor bowl as needed. Pour pulp through a fine wire-mesh strainer placed over a medium bowl, and press on solids with a rubber spatula to extract ⅓ cup liquid; discard solids and any excess liquid. Set aside.

Heat coconut milk in a medium saucepan over medium-low, stirring occasionally, until steaming. Remove from heat. Stir in ⅔ cup shredded coconut and reserved pandan liquid; let stand at room temperature until flavors infuse and mixture has cooled, about 30 minutes.

Beat sugar and butter in bowl of a stand mixer fitted with the whisk attachment on medium speed until light and creamy, 3 to 4 minutes, stopping to scrape down sides of bowl as needed. Add eggs, 1 at a time, beating well after each addition.

Sift together flour, baking powder, and salt in a large bowl. With mixer running on low speed, gradually add flour mixture to butter mixture alternately with coconut milk mixture, beginning and ending with flour mixture; beat until just combined. Divide batter evenly between prepared pans; smooth tops using an offset spatula.

Bake in preheated oven until a wooden pick inserted in center of cakes comes out clean, 35 to 40 minutes. Let cakes cool in pans on a wire rack 5 minutes. Remove cakes from pans; let cool completely, parchment side down, on a wire rack, 2 to 3 hours. Remove and discard parchment.

Stir 1 ¼ cups mascarpone in a medium bowl until loosened to a spreadable consistency; swirl in jam. Trim top of 1 cake layer using a serrated knife to create a flat surface; place cake layer, cut side up, on a serving plate. Spread mascarpone mixture evenly over top; cover with remaining cake layer, rounded side up.

Stir remaining mascarpone (about ½ cup) to loosen; spread evenly over top of cake.

Toast remaining 2 tablespoons shredded coconut in a small skillet over medium, stirring often, until golden brown, 2 to 3 minutes. Transfer toasted coconut to a small bowl, and let cool completely, about 15 minutes. Sprinkle toasted coconut evenly over cake.