Everything-Bagel Strata with Caper Relish and Smoked Salmon

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Everything-Bagel Strata:

8 ounces cream cheese, at room temperature

8 large eggs 

2 1/2 cups milk 

1/4 cup grated Parmesan 

Kosher salt and freshly ground black pepper 

1/4 cup chopped fresh dill 

1 teaspoon grated lemon zest 

5 day-old everything bagels, halved horizontally and cut into bite-size pieces 

Butter, for greasing the baking dish

Caper Relish:

2 tablespoons capers

2 tablespoons chopped fresh dill, plus fronds for garnish 

1 pint grape tomatoes, halved 

1/2 small red onion, finely diced 

Kosher salt and freshly ground black pepper 

4 ounces smoked salmon, thinly sliced