Heat the oven to 400°F.
Tear the rolls into roughly 1-inch pieces. Spread the pieces on a sheet pan and toast in the oven until crisp but still soft, about 5 minutes.

• Meanwhile:

• Peel and thinly slice the shallots.
• Wash and coarsely chop the kale.

In a 12-inch frying pan over medium-high heat, warm 1 tablespoon oil until hot but not smoking. Add the shallots, season with salt and cook until softened, about 5 minutes. Add the kale and the spinach, reduce the heat to medium and cook, stirring occasionally, until almost all the liquid has evaporated, about 5 minutes.

In a large mixing bowl, whisk the eggs, milk, mustard and nutmeg until well blended. Add the toasted pieces of the rolls and the kale mixture to the custard and, with a wooden spoon or a spatula, stir to combine. Let stand until the rolls have absorbed most of the custard.

Butter or oil a 9x5-inch baking dish. Put half the strata mixture in the dish and sprinkle half the Swiss cheese and the parmesan on top. Repeat with the remaining strata mixture and the rest of the cheese. Bake until puffed and brown, 20 to 25 minutes.
While the strata bakes, make the salad.

• Pick the parsley leaves from the stems. Discard the stems.
• Chop the almonds.
• In a small bowl, combine the parsley leaves and the almonds.

Just before serving, toss the parsley salad with the vinegar, a splash of olive oil and season with salt. Cut the strata in half, transfer to serving plates and serve the parsley salad alongside.