Put a large pot of water over high heat and bring to a boil.
Salt the water generously, and then add the pasta. Cook for 8-12 minutes, or according to package directions, until the pasta is just al dente.
In the last minute of cooking, add the peas to the cooking water.
Scoop a large cup of the pasta water out of the pot, and set it aside.
Turn the stove to low, drain the pasta and peas, and then set the same pot back on the still-warm burner.
Add the olive oil and garlic to the pot and stir for a moment to combine. Cook for 1-2 minutes until the garlic is just barely starting to brown.
Add the yogurt and parsley, and stir to combine well.
Add the pasta and peas, and stir to combine well.
If the yogurt sauce is too thick, add some pasta water, 1 tablespoon at a time, until the sauce has reached the desired consistency.
Season with salt and pepper, remove from the heat, and serve immediately.