Place the purified tallow in a heat-safe bowl. Set the bowl over a saucepan with a few inches of gently simmering water to create a double boiler.
Melt the tallow completely, then remove from heat. Stir in the olive oil or jojoba oil until fully combined.
Allow the mixture to cool at room temperature until opaque but still soft. Using a hand mixer or stand mixer, whip for 2 to 5 minutes, or until light and creamy. If using vitamin E or essential oils, add them during whipping.
Spoon the whipped tallow cream into a clean glass jar and seal.
If you prefer a firmer texture, you can also pour the melted mixture into jars without whipping. For a full balm-style recipe, see my Homemade Whipped Tallow Balm DIY Recipe.