Pierce potatoes all over with a fork. Microwave on high for 4 minutes, then transfer to a rimmed baking sheet and bake until soft inside, about 45 minutes.
While the potatoes are baking, combine the beans, mayo, garlic, shallot, olive oil, chives, lemon juice, mustard, salt, pepper and vinegar in the bowl of a food processor and puree until very smooth, scraping down the sides of the bowl as needed. Transfer to a large bowl.
When the potatoes are ready, let them cool for a few minutes until they're easy to handle and increase the oven temperature to 450F.
Slash open the potatoes and use a fork to flake flesh into the bowl with the bean mixture. Gently mix in the potatoes to incorporate. Let the mixture stand for 20 minutes so the potatoes can absorb the moisture. At this point the mixture can be refrigerated in an airtight container for up to a week before being baked.
Transfer the mixture to a 3- to 4-cup gratin dish or small casserole. Bake until the top is bubbly and lightly browned, 15 to 20 minutes.