Bring 3 quarts of water in a large pot to a boil. Once boiling, carefully lower eggs and bring back to a boil (about 30 seconds). Cover the pot with a tight-fitting lid and reduce the heat to just simmering. Cook for 11 minutes.

Transfer eggs to a large bowl of ice water and set aside until chilled, about 10 minutes.

Drain well, peel under cool water and halve eggs. Transfer whites to a platter and yolks to a large bowl.

Meanwhile, cook bacon in a large skillet over medium heat until crisp, 8 to 10 minutes.

Transfer to a paper towel-lined plate and crumble into large pieces when cool enough to handle.

To the cooked yolks, add yogurt, mayonnaise, mustard, lemon juice, salt, pepper and shallot, and mash with a fork until well combined.

Pile some of the yolk mixture into the middle of each egg white, top with a tomato half, a piece of bacon and a pinch of lettuce, and serve. (Make and fill eggs ahead, if you like, but wait to garnish with bacon, tomatoes and lettuce until just before serving.)