Preheat oven to 350°F (180°C). Grease a 13 x 9-inch (3.5 L) rimmed baking sheet or metal cake pan with butter and line bottom with parchment paper.
In a food processor or high-speed blender, combine sugar and butter; process until blended and fluffy. Add eggs and ube; purée until incorporated and mixture is smooth.
In a large bowl, whisk flour and baking powder. Add ube purée and fold until just combined. Pour into prepared pan and smooth top.
Bake for about 15 minutes or until a toothpick inserted into the centre comes out clean. Let cool in pan for 5 minutes, then invert onto a wire rack and peel off parchment. Let cool completely on rack.
Transfer cake to cutting board. Cut in half crosswise, then lengthwise to make 4 equal rectangles. Cut each rectangle crosswise into 6 bars to make 24 bars total.
Spread coconut onto a plate. Holding a cake bar in one hand and using a pastry brush in the other, lightly coat each bar all over in condensed creamer. Using your clean hand, roll cake bar in coconut, turning and pressing lightly to coat evenly. Let set on a cooling rack. Repeat with remaining cake bars, creamer and coconut.
Serve immediately or store lightly covered at room temperature for up to 4 days.
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