Crack 1 egg into a blender. Add 1 cup ketchup, 1/2 cup white vinegar, 1/2 cup sugar, 1/2 tablespoon salt, and 2 tablespoons paprika. Secure the lid.

Blend briefly on medium speed until the ingredients are smooth and well combined.

With the blender running on low to medium speed, slowly drizzle in 2 1/2 cups salad oil in a thin, steady stream through the lid opening. Continue blending until the mixture thickens and becomes a smooth, fully emulsified dressing.

Stop the blender, pour the dressing into a clean container, and refrigerate until chilled before serving.