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Preheat oven to 350 degrees F. Line 8x8-inch pan with parchment paper.
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In mixing bowl, whisk together almond flour, tapioca flour, coconut flour, baking powder and salt.
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In another bowl, beat eggs and coconut sugar until light and fluffy, about 2-3 minutes. Add coconut milk, melted coconut oil and vanilla extract; mix well.
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Gradually fold in dry flour mixture until just combined.
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Pour into prepared pan and bake 25-30 minutes or until toothpick inserted in center comes out clean.
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Let cake cool completely before slicing in half horizontally.
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In small saucepan over medium heat, combine raspberries, coconut sugar, maple syrup, lemon juice and water. Simmer 5-7 minutes, mashing berries as they break down. Stir in chia seeds and let jam thicken 5 minutes. Remove from heat and cool completely.
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Carefully slice cooled cake in half horizontally.
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Spread jam evenly over one half, then place other half on top. Freeze cake 30 minutes for ease of coating.
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In small saucepan over low heat, whisk together all coating ingredients until smooth. Remove from heat and let cool slightly.
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Slice chilled cake into squares. Add shredded coconut to shallow bowl or plate. Use fork or dipping tool to dip each square into melted chocolate mixture and then roll them in coconut, coating entire square. Place Lamingtons on wire rack or parchment-lined tray and refrigerate at least 30 minutes to set fully.
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Refrigerate in airtight container up to 5 days. Freeze up to 3 months; thaw at room temperature before serving.