Cut away the green stem end from the chili, split it lengthwise, discard the seeds, and chop finely with a knife. If you have the mortar and pestle, put the garlic, egg yolks, chili, lemon juice, salt, and pepper in the mortar and pound with the pestle until the mixture thickens lightly, about 1 minute. Pounding develops the flavor of the chili and garlic. Gradually beat in the oil a few drops at a time until the sauce starts to thicken and emulsify. After adding about 2 tablespoons of the oil, the mixture should be quite thick. Transfer it to a small bowl and continue adding the remaining oil more quickly, pouring it in a very slow, thin stream while stirring constantly with a whisk or an immersion blender. (If added too quickly, the sauce may separate.) If you are not using a mortar and pestle, whisk the sauce in a bowl from the start. Work in the tomato paste and vinegar, taste, and adjust the seasoning. The sauce may be covered tightly and stored in the refrigerator for no more than 12 hours. At serving time, let it come to room temperature before you stir it or it may separate.