Preheat the oven to 425 degrees . Using a pastry brush, coat the mushroom caps with EVOO. Place on a baking sheet and bake, top side up, until tender but firm, about 8 minutes. In a large bowl, combine the artichokes, spinach, ricotta, egg yolk, garlic and nutmeg; season with salt and pepper.
Divide the stuffing evenly among the mushroom caps. Sprinkle with the parmigiano-reggiano and cook until the filling is set and lightly browned, about 5 minutes.
Place the tomatoes in a salad bowl. Add the bread, onion, basil, the remaining 1/4 cup EVOO and lots of salt and pepper. Toss to combine. Serve 2 mushroom caps per person with a pile of bread salad alongside.