Place the garlic, mustard, egg yolks and dill in the bowl of a mini-food processor, or blender. Process until evenly combined, about 10 seconds.
With the motor running, slowly add the olive oil in a thin stream until completely combined. This should take about 2 minutes so drizzle very slowly and make sure you don't add more than ¼ cup in the first 30 seconds.
Once you have a thickened sauce, stop the processor, add the lemon juice, season with salt/pepper and pulse until thoroughly mixed and with a thick consistency. Stop and scrape down the sides of the bowl with a rubber spatula, then pulse until all ingredients are evenly incorporated. Let sit for at least 30 minutes before using. Refrigerate in a container with a tight fitting lid for up to one week.