Adjust oven rack to middle position and preheat oven to 350°F. Line bottom of 10-inch tube pan with parchment paper. Place chopped pandan leaves in food processor and add 2 tablespoons water. Blend until leaves are pulverized, about 1 minute (add an extra tablespoon water if mixture is too thick to blend). Strain mixture though cheesecloth, squeezing tightly to extract as much juice as possible. You should have 3 to 4 tablespoons juice.
In large bowl, whisk 6 yolks with 1/2 cup sugar until very light, about 1 minute. Whisk in oil until combined. Whisk in coconut milk, pandan extract, and 3 tablespoons pandan juice until combined.
Sift cake flour, baking powder, and salt into medium bowl. Gently whisk flour mixture into pandan mixture until smooth.
Using standing mixer fitted with whip attachment, beat 9 egg whites on medium low speed until frothy. Add cream of tartar, increase speed to medium, and continue to beat until meringue begins to look opaque. Increase speed to medium high and slowly add remaining 1/2 cup sugar. Continue to beat until meringue reaches stiff but not dry peak.
Fold 1/3 of meringue into batter until combined. Carefully fold in remaining meringue in two stages until just combined, being careful to not deflate meringue.
Pour batter into ungreased 10-inch tube pan and bake until cake is golden on top, set, and long skewer inserted into the center comes out clean, about 45 minutes. Completely cool cake in pan, about 2 hours. Invert onto serving plate to serve.