This approach makes pesto that's less grassy and intense than raw basil versions, with rounded, balanced flavor. It's good to use a mellow, mild olive oil here so it doesn't detract from the fresh herbs. We also prefer Parmigiano-Reggiano cheese in pesto because it’s milder than super-sharp sheep’s-milk pecorino romano. If you don't care for the hot taste of raw garlic, you can take the edge off the cloves by blanching them along with the basil. We use sunflower seed kernels here because they are far less expensive than the pine nuts traditionally used, and their flavor is similarly rich and sweet. If you have pine nuts already on hand, feel free to use them instead.
Bring a large Dutch oven filled with water to a boil over high. Fill a large bowl with ice water. Place basil leaves in a metal strainer. Place strainer in pan, using tongs to quickly submerge all basil leaves; cook 5 seconds or just until leaves turn bright green. Carefully remove strainer with leaves from pan; drain. Immediately plunge strainer with leaves in ice water bath. Let stand 10 seconds. Remove basil; drain well. Spread basil leaves on a clean, dry dish towel; gently blot dry with another towel.
Place basil, sunflower seeds, oil, salt, and garlic in a food processor; process until smooth. Add cheese; process until blended.