Add the beef tallow and olive oil or avocado oil to a double boiler. Warm gently over low heat until everything is fully melted and combined. Stir occasionally and avoid overheating the mixture. You only need enough heat to melt the tallow.
Remove the melted mixture from the heat. If you are using vitamin E oil or essential oils, let the mixture cool slightly before adding them. Pour the mixture into a shallow bowl and let it cool until it begins to thicken. It should look soft and semi-solid, not fully hardened.
Use a hand mixer or stand mixer with a whisk attachment to whip the balm for 3 to 5 minutes.
Whip until it becomes light, airy, and creamy. The finished texture should look similar to whipped butter.
Spoon the whipped tallow balm into a clean glass jar. Add the lid and store it in a cool, dry place away from direct sunlight.