Sprinkle half the rosemary and thyme leaves all over the inside of each butterflied and pounded pork tenderloin and spread the prosciutto evenly in one layer over the herbs. Beginning with the long end, roll up the tenderloin tightly, tucking in the ends (as you would a burrito). Use kitchen twine to tie the roll in a bundle, tying it every 2 inches.
In a large nonstick skillet over medium-high, heat 1 tablespoon of the oil. Season the pork lightly on all sides with salt and pepper, then add it to the skillet. Sear until golden brown on all sides. Transfer the pork to a shallow baking pan, then roast on the oven's middle shelf until the center reaches 145 F, about 20 to 25 minutes. Remove the pork from the oven and cover loosely with foil.
Meanwhile, make the sauce. Return the skillet to medium heat. Add the remaining 2 tablespoons of oil and the shallots and cook, stirring, until the shallots are golden. Add the mushrooms and cook, stirring often, until the mushrooms give off all their liquid and are lightly browned.
Add the Marsala and simmer until almost all of it is reduced. Add 1 cup of the chicken broth and bring back to a boil. In a small bowl whisk the remaining 1/4 cup of chicken broth with the flour. Add the flour mixture to the skillet in a stream while whisking and simmer for 2 minutes. Add any juices that have accumulated from the resting pork to the sauce.
Slice the pork crosswise into 1-inch-thick slices. Transfer several slices to each of 6 serving plates. Spoon some of the mushroom sauce over each serving.
Nutrition information per serving: 330 calories; 110 calories from fat (33 percent of total calories); 13 g fat (3 g saturated; 0 g trans fats); 115 mg cholesterol; 9 g carbohydrate; 1 g fiber; 3 g sugar; 39 g protein; 770 mg sodium.