Combine the tomatoes, shallots, garlic, mustard, salt, white pepper, and stock in a nonreactive saucepan over high heat and bring to a boil, stirring occasionally. Cook for 2 minutes, remove from the heat, and allow to cool for about 15 minutes.
Pour the mixture into a food processor or blender, add the egg, and turn on the machine. Stream in the oil and process until very smooth, for about 45 seconds. Stir in the black pepper. Serve immediately.
Yield: 1 1/4 cups