Fill a large, wide pot with about 3 inches of water and a hefty splash of vinegar. Bring to a low simmer.
Meanwhile, heat 1 tablespoon of the oil in a large nonstick skillet. Add the onions, bacon, a pinch of salt and a few grinds of pepper, and cook, stirring frequently, until the onion and the bacon are browned in spots, about 5 minutes. Remove from the heat, and let cool.
Put the remaining 2 tablespoons oil and the vinegar, lemon zest and juice, yogurt, 1 tablespoon water and 1/4 teaspoon salt in a jar or other container with a lid. Secure the lid, and shake well to combine. (The dressing can be made a day ahead; shake well before serving.)
Toss the greens, tomatoes, onion-bacon mixture and dressing in a large bowl. Add salt to taste. Divide among 4 salad bowls.
Toast the English muffins, and cut each in half.
Crack 1 egg into a small bowl. Swirl the simmering water, then gently slide the egg into it. Repeat with the remaining eggs. Cook until the whites are set and the yolks are still runny, 3 to 4 minutes. Remove the eggs with a slotted spoon, and place 1 on top of each salad. Garnish each salad with 2 English muffin pieces and a few grinds of pepper.
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