Heat oven to 450°. On a rimmed baking sheet lined with parchment paper, place caps4 top up. In a bowl, whisk 2 teaspoons oil4 teaspoons and vinegar2 teaspoons and season with salt and black pepper. Brush caps with oil mixture; reserve remaining mixture. Bake until tender, 8 minutes. In a skillet over medium heat, heat remaining 2 teaspoons oil. Cook shallots1/4 cup until soft, 2 minutes. Add garlic2 teaspoons and rosemary1 teaspoon; cook, 1 minute. Stir in beans1 can and broth1/4 cup; season with black pepper. Remove from heat, stir in prosciutto1 ounce and parsley2 tablespoons and transfer to a bowl. In the same skillet over medium heat, cook spinach3/4 cup until wilted, 1 minute. Drain juice from caps and return to baking sheet, top down; brush with remaining oil mixture. Stuff caps with bean mixture and spinach. In a bowl, combine panko and Parmesan2 tablespoons; divide among caps. Coat caps with cooking spray; bake until panko is golden, 10 minutes.