In the bowl of a food processor or blender, combine 5 tablespoons olive oil, the yogurt, ⅔ cup peas, the grated garlic and 1 teaspoon salt. Pulse until the sauce is no longer chunky, scraping the sides with a rubber spatula. Transfer to a large bowl and set aside.
Bring a large pot of well-salted water to boil. Add pasta and cook until al dente according to the package directions. Drain.
While the pasta is boiling, add the sliced garlic to a large skillet, along with the remaining 3 tablespoons olive oil, ¼ teaspoon red-pepper flakes and a big pinch of salt, and place over medium heat. Cook, stirring occasionally, until the garlic turns golden at the edges, 2 to 5 minutes.
Add the asparagus and remaining ⅓ cup peas to the skillet and sauté until just cooked through, 2 to 3 minutes. If the pan looks dry, add a tablespoon or two of water.
After draining, add the warm pasta to the yogurt mixture in batches, stirring in between, so the sauce doesn’t curdle. Stir in the asparagus mixture, feta, remaining ¼ teaspoon red-pepper flakes and the lemon juice. Taste and add more salt, red-pepper flakes, or lemon juice if needed. Drizzle with olive oil, garnish with mint leaves and scallions, and serve warm.
