1) Heat the oven to 450 degrees F. Meanwhile, add 1-2 tbsp olive oil to large pot over medium-high heat. Add leeks and cook for 3 to 5 minutes till browning begins, stirring occasionally. Add garlic and rosemary and cook for another minute, stirring occasionally. Add salt and pepper and stir to loosen vegetables that have stuck to the bottom of the pan.
2) Add potatoes, bean, and stock. Cook on medium heat so that mixture is bubbling steadily. Cover partially and cook, stirring occasionally, until potatoes are disintegrating, 20 to 30 minutes. Add more stock as necessary for desired thickness.
3) Meanwhile, drizzle asparagus in olive oil and salt liberally, and then roast on baking sheet for about 10 minutes. Let cool and chop asparagus. Mash potatoes and bean soup mixture with a potato masher to desired consistency (optional). Add asparagus to soup and top each bowl of soup with cheese. Serve immediately.