Preheat the oven to 350 degrees . Brush an 8-cup baking dish with 1 tsp. EVOO; add the bagel pieces in an even layer.
In a nonstick skillet, cook the pancetta over medium until almost crispy, about 5 minutes. Using a slotted spoon, transfer to a bowl.
Add the butter to the drippings in the skillet and melt over medium. Add the onion and cook, stirring occasionally, until beginning to brown, about 12 minutes. Season with salt and pepper; spoon over the bagel pieces.
Whisk the milk, eggs, cream, nutmeg, 1/2 tsp. salt and 1/4 tsp. pepper with the pancetta. Stir in 1 cup cheese; pour over the bagel mixture, pressing to submerge bagels. Sprinkle with the remaining 1/2 cup cheese. Let stand at least 10 minutes. (Strata can be covered and chilled overnight before baking.)
Bake until golden and just set, about 45 minutes.
In a bowl, toss the lettuce, radishes, vinegar and the remaining 4 tsp. EVOO; season. Serve with the strata.