Bring a medium sauce pot of generously salted water to a boil. Add the orecchiette and cook until just tender, 10 to 15 minutes. Drain, reserving ½ cup [¾ cup] pasta cooking water. Return the orecchiette to the pot, drizzle with 2 to 3 teaspoons oil, and toss to keep the orecchiette from sticking.
While the water heats and the orecchiette cooks, prepare the prosciutto and start the sauce.

• Coarsely chop the prosciutto.

In a large frying pan over medium-high heat, warm 1 teaspoon [2 tsp] oil until hot but not smoking. Add the prosciutto and cook, stirring occasionally, until lightly browned and crisp, 4 to 5 minutes. Transfer to a paper-towel-lined plate. Pour off all but 1 tablespoon oil from the pan.
While the prosciutto cooks, prepare the remaining ingredients.

• Snap off the woody ends from the asparagus; cut the asparagus on the diagonal into 1-inch lengths.
• Finely chop, press, or grate enough garlic to measure 1 teaspoon [2 tsp].
• Coarsely chop the olives.

In the same pan used for the prosciutto, warm the residual oil over medium-high heat until hot but not smoking. Add the asparagus, season lightly with salt and pepper, and cook, stirring occasionally until crisp-tender, 3 to 4 minutes. Stir in the garlic and cook until fragrant, about 30 seconds. Stir in the tomato paste and cook until starting to darken, about 1 minute. Add the olives and reserved pasta cooking water and cook, stirring occasionally, until the asparagus is tender and the sauce is thickened, 3 to 4 minutes.
Remove from the heat and stir in the peas, prosciutto, and orecchiette. Season to taste with salt and pepper.

Transfer the orecchiette and sauce to individual plates. Crumble the ricotta salata on top, sprinkle with as many chile flakes as you like, and serve.