In a small saucepan, warm olive oil, 4 thyme sprigs, and salt on low heat(it should not simmer or bubble), for 10 minutes. Remove from heat and set aside. Meanwhile, add shallots to a glass jar with lid, and pour vinegar over the top. Let sit while olive oil is warming, about 10-15 minutes.
In a large bowl combine black pepper, white beans, and apples.
When shallots are done marinating, remove thyme from olive oil, and pour this over the top of shallots. Then remove leaves from remaining two sprigs of thyme, mince, and add to jar. Shake with top on jar, to combine. Pour over apples and beans, and stir thoroughly to combine. Let sit at room temperature for a minimum of twenty minutes, and serve, or you can refrigerate, and eat whenever you're ready, giving it time for the flavors to mingle.
Once refrigerated, it will need about 10 minutes at room temperature before you eat it, for the olive oil to warm into liquid again. (If your olive oil does not harden in the refrigerator, that is a sign you are using a fake olive oil.) Can be made 2 days ahead, and will last for 4 days in refrigerator.