Combine garlic, basil and nuts in bowl of a food processor or a blender and process until finely chopped, scraping down sides of bowl once or twice. With motor running, add olive oil in a slow, steady stream. Scrape mixture into a small bowl and stir in cheese and yogurt. Season with salt. Cover with plastic and refrigerate for up to 3 days, until ready to use.
Bring a large pot of salted water to a boil and cook pasta until al dente. Reserve 1/2 cup cooking liquid. Drain pasta and return to pot. Toss with pesto. If pasta looks too dry, add reserved cooking liquid, 1 Tbsp. at a time, to moisten. Season with salt and pepper to taste. Serve immediately.