Ricotta salata is an aged salted ricotta cheese. You can substitute another salted, crumbly cheese, such as feta.
Make the salad: Juice 1 lemon into a large bowl filled with water. Remove tough outer leaves of artichokes, cut off top two-thirds, and scoop out fuzzy chokes with a spoon; discard. Cut each in half, transferring to lemon water as you work to prevent discoloration.
Bring milk, 3 cups water, and white asparagus to a simmer in a medium saucepan over medium-high heat. Reduce heat to medium-low, and cook until tender, skimming foam, about 45 minutes. Transfer to a paper-towel-lined plate; let drain and cool.
Bring prepared artichokes, wine, remaining lemon (squeezed, with rind), and remaining 2 cups water to a boil in a medium saucepan. Reduce heat, and simmer until tender, 13 to 16 minutes. Using a slotted spoon, transfer artichokes to a paper-towel-lined plate; let drain and cool. Discard lemon.
Meanwhile, prepare an ice-water bath. Bring a large saute pan of water to a boil. Add green asparagus, and cook until tender, 4 to 6 minutes. Transfer to ice-water bath, and let cool; reserve cooking liquid. Drain asparagus on a paper-towel-lined plate. Add fava beans to boiling cooking liquid, and cook until tender, 3 to 5 minutes. Transfer to ice-water bath, let cool, then squeeze beans from skins. Divide beans and vegetables among 8 plates. Sprinkle with mint and ricotta salata.
Make the dressing: Puree all the ingredients in a food processor until smooth. Drizzle over salads, and serve.