Heat the oven to 190 C / 375 F with a rack in the middle. Pass the banana leaf over a low gas flame for a few seconds per side, or dip it in hot water for 30 seconds, until glossy and pliable. Trim it to a 30 cm / 12-inch round, press it into a 23 cm / 9-inch round cake pan (5 cm / 2 inches deep) and brush with 1 tablespoon of the melted butter.
Whisk the glutinous rice flour, regular rice flour, 120 g sugar, baking powder and salt in a large bowl. In a jug, whisk the coconut milk, whole milk, eggs and 60 g melted butter until smooth.
Pour the wet ingredients into the dry and whisk until no lumps remain. The batter should be thin and pourable, about the consistency of heavy cream. Pour it into the pan and tap the pan on the counter twice to knock out large bubbles.
Bake for 25 minutes, until the top is set and the edges look pale gold and pull slightly from the pan.
Arrange the salted egg slices on top, then scatter the cheddar and shredded coconut. Bake for 8 more minutes until the cheese melts. Switch the oven to broil and broil for 3 minutes, watching closely, until the top is spotted golden brown. Insert a toothpick in the center. It should come out clean. If it's wet with batter, bake 5 more minutes at 190 C / 375 F, because a cake pulled too early turns gummy in the middle.
Brush the top with the remaining 1 tablespoon melted butter and sprinkle with 2 tablespoons sugar. Cool in the pan for 10 minutes, lift out, cut into 8 wedges and serve warm.