Blend the pandan leaves with 120 ml water in a high-speed blender for 1 to 2 minutes, until a green slurry forms. Strain through a fine-mesh sieve, pressing hard on the pulp, and measure out 70 ml juice. Discard the rest. Heat the oven to 170 C / 340 F with a rack in the middle, and line the bottoms of two 20 cm / 8-inch round cake pans (5 cm / 2 inches deep) with parchment. Leave the sides ungreased.
In a 3 L / 3-quart mixing bowl, whisk the 6 egg yolks with 50 g of the sugar for 1 minute until pale. Whisk in the oil, coconut milk, pandan juice and 1/4 tsp salt. Sift the cake flour and baking powder over the bowl and whisk for about 1 minute until the batter is smooth and lump-free.
Beat the 6 egg whites with the cream of tartar in the 4.7 L / 5-quart bowl of a stand mixer on medium speed until foamy, about 1 minute. Add the remaining 80 g sugar a tablespoon at a time, then whip on medium-high for 3 to 4 minutes, until glossy and the peak stands upright with a slight curl at the tip. Stop there. Dull, grainy whites are overwhipped and will clump when folded.
Stir a third of the whites into the yolk batter to loosen it, then fold in the rest in two additions, scraping the bottom of the bowl, until no white streaks remain. Divide the batter between the pans (about 380 g each) and tap each pan once on the counter. Bake for 22 to 25 minutes, until a skewer comes out clean and the top springs back when pressed lightly.
Cool the layers in their pans for 10 minutes, run a thin knife around the edges, and turn them out onto a rack. Peel off the parchment and cool completely, about 60 minutes. While they cool, toast the 80 g coconut flakes in a dry 26 cm / 10-inch skillet over medium-low heat for 4 to 5 minutes, stirring often, until light gold. Tip onto a plate to cool.
Wash and dry the mixer bowl and whisk. Beat the cold mascarpone, powdered sugar, coconut extract and a pinch of salt on low for 30 seconds until smooth. With the mixer running, pour in the cold cream, then whip on medium-high for 2 to 3 minutes until it holds stiff peaks.
Set one layer on a plate or cake stand, spread it with about 1 cup / 240 g of the frosting, and scatter 20 g of the toasted coconut over it. Top with the second layer, flat side up. Frost the top and sides with the remaining cream, then press the rest of the toasted coconut (about 60 g) onto the sides and top. Chill for 60 minutes.
Slice with a long knife warmed in hot water and wiped dry between cuts, making 12 wedges. Serve straight from the fridge.