Bring a large pot of water to boil. Add 1 tbsp. salt and penne. Cook until barely tender to the bite. Drain; set aside.
In the same pot, heat olive oil over high heat. Add mushrooms and remaining tsp. salt and cook, stirring constantly, until mushrooms stop giving off liquid and start to brown, about 10 minutes. Turn heat to medium-high and add garlic. Cook, stirring, until fragrant, about 2 minutes. Stir in chicken broth and penne and cook until broth is absorbed. Stir in cheese until melted and coating the pasta. Take off heat and stir in mint. Serve immediately, topped with prosciutto and pepper.
Note: Nutritional analysis is per serving.