In a small food processor or cup using an immersion blend, whisk together the 2 large egg yolks, 2 teaspoons fresh lemon juice and 2 grates lemon zest, and 1 teaspoon Dijon mustard. Pulse, scraping down the sides, until it becomes a pale yellow paste.
While whisking or while the immersion blender is on, very slowly pour the 1/2 cup extra-virgin olive oil into the yolk mixture. It should start to thicken and combine, but if it it does seperate, stop adding the oil and continue to whisk until it combines again, then resume the oil.
When fully combine, add the grated 2 cloves garlic* and 1/8 teaspoon fine sea salt, either giving a few more quick pulses or folding in by hand.
Cover and refrigerate for 1 hour to let flavors marry.
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Notes
*grated garlic is optional, if making a roasted garlic aioli, omit this and only add the roasted garlic.