Heat a cast-iron pan over medium-high flame. Brush two thick slices of sourdough with olive oil and sear until browned. Place on a plate and sprinkle with Parmigiana-Reggiano while the bread is still hot. Set aside.
If using extra long, wild asparagus, trim down until each stalk is about 10-12 inches long. Save the rest of the stalks for another use. In a large pot of salted boiling water, blanche the asparagus for 3 minutes. Using tongs, immediately transfer to a bowl of ice water.
Roll the kale to break down their fibrous leaves, and then slice very thinly. Toss with olive oil, salt, and a squeeze of lemon juice.
To assemble the salad, break apart two of the bread slices with your hands into 1 to 2-inch chunks. Sprinkle evenly on an oval-shaped platter. Sprinkle the kale on top of that. For the next layer, lay the asparagus so that it covers the kale and toasted bread. Sprinkle with the Japanese turnips and herb mix. Drizzle a healthy bit of good olive oil over it, top with ricotta salata and torn bits of the remaining bread.