- Fill a large skillet halfway up with water and bring to a boil. Add vinegar; reduce heat so water is barely simmering.
- One at a time, break eggs into small cup, then slide into water. Cook eggs until whites set, about 4 minutes; with slotted spoon, transfer eggs to paper towels to drain.
- Pour out water and wipe skillet dry; add bacon and cook over medium-high heat, turning once, until bacon is heated through, about 1 minute per side.
- To make sauce, whisk mayonnaise, yogurt, mustard, lemon zest, and lemon juice together in small microwavable bowl; microwave on High until hot, about 30 seconds, then stir in butter until melted
- Top each toasted muffin half with 1 slice tomato, 1 slice bacon, an egg and about 2 tablespoons sauce; sprinkle with chives.
- serving: 1 open-faced sandwich
If you want to poach the eggs ahead, take them out of the poaching water about 1 minute earlier and slip them into a bowl of ice water. Refrigerate them in the water up to 1 day; reheat them gently in simmering water