Bring a large pot of salted water to boil for the pasta. Add the olive oil to a large skillet over medium heat. When the oil is hot, add the garlic and let it sizzle a minute. Add the asparagus and toss to coat in the oil. Cook and toss until the asparagus just begins to soften, about 5 minutes (add a splash of pasta water if the garlic is in danger of burning). Cover with a lid.
Uncover the asparagus, and at the same time add the orecchiette to the pasta water. Add the peas to the asparagus and season with the salt. Toss to combine and cook 2 to 3 minutes. Add the scallions, stir, and add 1 1/2 cups of pasta water. Bring to a boil and cook until reduced by about half, 3 to 4 minutes.
When the pasta is al dente, remove with a spider directly to the sauce. Add the parsley, drizzle with some olive oil, and toss to coat the pasta in the sauce, adding a little pasta water if it seems dry. Remove the skillet from the heat, sprinkle with the grated cheese, toss, garnish with pea tendrils and serve.