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Make the coconut oil mayonnaise - add the egg yolks into a blender and whisk until smooth.
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Add the lemon and mustard, and process to incorporate.
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Add gradually the olive oil while processing at low speed. Continue the same with the coconut oil.
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Season with salt, transfer into an airtight jar and refrigerate.
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Add the diced cucumbers and carrots into a bowl, together with the rice vinegar and freshly ground pepper, mix and set aside.
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Mix the tamari and coconut oil into a small bowl, cut the firm tofu into 1/2 inch slices and soak into the mixture.
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Heat a non stick skillet over medium heat, then add the marinated tofu slices and cook for four or five minutes on each side, until golden. Remove and set aside.
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Assemble the sandwiches with tofu, marinated cucumbers, carrots and mayonnaise.
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Add fresh cilantro or parsley leaves, then serve.