Combine the oils in a liquid measuring cup. In a food processor, combine the tomato paste, garlic, egg yolks and ½ teaspoon salt. Process until light yellow in color, 1 to 2 minutes, scraping the bowl as needed.

With the machine running, dribble in the oil mixture a few drops at a time to start. As the mixture thickens, gradually increase the rate at which you add the oil. As you add more oil, the mixture will become increasingly thick; scrape the bowl as needed. If it begins to clump, drizzle in a few a drops of water, up to 1½ tablespoons, as needed to thin the consistency.

Once all the oil is incorporated, taste and season with salt. Transfer to a small bowl, cover with plastic and let stand for 1 hour before using. Refrigerate for up to 5 days.