Pour the egg yolks into a bowl and mix with the garlic, mustard, and some of the lime juice.
Adjust the seasonings with salt, and pepper and, using an electric hand mixer or whisk, beat the ingredients and gradually start to add the oil, one drop at a time. Keep adding the oil until the mixture thickens, and emulsifies. If the mayonnaise looks like it might split or break, add a spoonful or so of warm water and stir it in. This usually "brings it back." If you find that your mayonnaise is too thick, add a little more warm water until you achieve the desired consistency.
Stir in the chile, including the seeds (adding a few seeds at a time, depending on the desired heat), the cilantro, and the rest of the lime juice, to taste.
Reserve half of the chile seeds.
You probably won't need to use all of the lime juice.