Put the yogurt, 6 tablespoons of the olive oil (a little over 1/3 cup), the garlic, and about half of the peas in a food processor. Blitz to a uniform pale green sauce and transfer to a large mixing bowl.  Add some salt and a bit of white pepper and taste.  Don't oversalt for now, but some seasoning is important.

Bring a large pot of water to a boil, salt heavily, and add the pasta.  Cook until al dente (usually 6-7 minutes).

As the pasta cooks, heat the remaining olive oil in a small frying pan over medium-low heat. Add the chile flakes and fry for a couple minutes to turn the oil a deep red, then add the pine nuts and cook for maybe a minute, stirring frequently (they'll burn in a second so watch carefully).

In the last 2 minutes of the pasta cooking, add the remaining peas to heat them up.

Drain the cooked pasta and peas into a colander, shake well to get rid of the water, and add it GRADUALLY to the yogurt sauce, stirring to toss.  Adding it all at once may cause the yogurt to split.

Add the basil, feta, and more salt and pepper.  Toss gently and taste, adjusting the seasoning as needed. 
Transfer to individual bowls, spoon the pine nuts and their oil over the bowls and serve.