The potatoes give this garlicky condiment some added heft.
Combine garlic and 1/2 cup oil in a small pot. Bring to a simmer over medium-high heat; cook until very tender, 5 to 7 minutes. Pour oil through a fine sieve into a bowl. Set aside garlic. Place potatoes in a pot; cover with 1 inch water. Bring to a boil. Reduce heat, and simmer potatoes until tender, about 12 minutes. Pass garlic and potatoes through a food mill into a bowl.
Stir in saffron, pepper flakes, and paprika. Stir in egg yolks. Beat in garlic oil and remaining 1 1/2 cups olive oil with a mixer until emulsified. Season with about 1 teaspoon salt. Rouille can be refrigerated up to 2 days. (Note: The egg yolks in this recipe are not cooked.)