Make the strata: Butter a 9-by-13-inch baking dish. Combine the cream cheese and eggs in a blender and blend until smooth. Add the milk and parmesan and blend until smooth. Season with salt and pepper. Add the dill and blend a few seconds, then blend in the lemon zest.
Transfer the custard to a large bowl. Add the bagel pieces and mix to coat, pressing on the bagels to totally submerge them in the custard. Transfer the mixture to the prepared baking dish. Cover and refrigerate overnight, pressing on the bagels a few times.
Preheat the oven to 350˚. While it heats, remove the strata from the refrigerator, uncover and place on a baking sheet. Bake until puffed and lightly golden brown around the edges and just set in the center, about 40 minutes. Let sit for 15 minutes.
Make the caper relish: Combine the capers, dill, tomatoes and onion in a bowl. Season with a touch of salt and pepper. Let sit at room temperature for 15 minutes.
To serve, cut the strata into large round circles (like a bagel!) and place on plates. Top with the smoked salmon and relish.