Bring a medium pot of salted water to a boil. Add the egg and boil for 3 minutes. Scoop the egg from the water and crack it over a small bowl, scooping all of the white and yolk out with a spoon. Transfer to a blender with ½ teaspoon salt, the mustards, vinegar, and Tabasco. Puree on low speed, slowly streaming in the oils until emulsified. Transfer to a squeeze bottle with a large tip or a piping bag, and reserve, kept warm.