In a bowl, whisk together the egg yolk, mustard, tomato paste, garlic and salt. Slowly add one-third of the oil, drop by drop, whisking constantly. When the emulsion begins to form a mayonnaise, drizzle in the remaining oil while whisking. Season with pepper. Whisk in the lemon juice and saffron.
Spoon the rouille into a serving bowl and refrigerate until ready to use. The rouille will keep for 5 days in an airtight container in the refrigerator.