Bring the egg yolk and oil to room temperature by letting them sit for 15 to 20 minutes before starting.

In the bowl of a food processor, combine the room-temperature egg yolk, lemon juice, Dijon mustard, salt, and pepper; pulse briefly to mix.

With the processor running, add the oil drop by drop for the first 30 seconds to start the emulsion.

Once the mixture becomes thick and pale (after about 1/4 cup of oil), pour the remaining oil in a slow, steady stream while continuing to process for 2 to 3 minutes until fully incorporated.

Stop the processor and add the minced garlic; pulse 3 to 4 times to distribute evenly.

Taste the garlic mayo and adjust seasoning by adding more salt, lemon juice, or garlic as needed.

Scrape the garlic mayo into a clean glass jar, seal with a lid, and refrigerate for at least 30 minutes before serving.

Store in the refrigerator for up to three weeks, stirring to recombine if any separation occurs.