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Prepare your food processor with the blade attachment.
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Crack your egg in the food processor, then add your Dijon mustard and your garlic clove.
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Put the lid on, and start blitzing.
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As the mixture is processing, slowly add your oil. Don't add the oil too fast or else the mayonnaise can split.
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Once you have added about half of your oil, take the lid off and scrape down the sides. Put the lid back on and continue to add the other half of your oil while blitzing.
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When you have added all of the oil, the mayonnaise should be nice and thick.
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Add your lemon juice, then season with salt and pepper (be careful not to add too much salt). Blitz one more time to finish the aioli.