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Preheat the oven to 350°F. Grease a 9" springform pan and line the bottom with parchment.
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To make cake: In a large mixing bowl, combine the flour, baking powder, baking soda, and salt.
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In a medium bowl, whisk together the oil, sugar, coconut milk, lemon zest, lemon juice, and vanilla.
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Add the wet ingredients to the dry and whisk to combine. Pour the batter into the prepared pan and bake for 32 to 35 minutes, until the top is golden brown, the sides just begin to pull away from the pan, and a cake tester inserted in the center comes out clean. Remove from the oven and let cool completely in the pan on a rack.
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To make the compote: Put the blueberries, lemon juice, sugar (taste your berries and use the lesser amount of sugar if they're sweet), and 2 tablespoons of water in a small saucepan and bring to a simmer, stirring occasionally until the berries soften.
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While the berries cook, combine the cornstarch with the remaining cold water. Mix until smooth, then stir into the blueberry mixture. Continue cooking as the compote thickens and goes from cloudy to translucent. Remove from the heat; the compote will thicken further as it cools.
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To make the topping: Combine all the ingredients until smooth.
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To assemble: Just before serving, remove the side from the pan and place the cake on a serving plate. Spread the topping over the cake. Stir the compote a little to loosen it, and spoon it into the center of the cake. Serve immediately.
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Storage information: Store, covered in the refrigerator, for up to 5 days.
