Cook the pasta: Bring a large pot of generously salted water to a boil. Add the linguine and cook according to the package directions until al dente.
Prepare the ingredients: While the pasta cooks, finely chop the garlic and walnuts.
Wilt the spinach: During the last minute of cooking, reserve ½ cup of the pasta cooking water, then add the spinach to the pot. Stir until the spinach is wilted.
Make the sauce: In a large mixing bowl, whisk together the Greek yogurt and feta cheese until smooth. Slowly whisk in the reserved hot pasta water until the mixture becomes creamy and well combined.
Drain the pasta: Drain the linguine and spinach thoroughly, then immediately transfer them to the bowl with the yogurt mixture. Toss until the pasta is evenly coated.
Add the seasonings: Stir in the chopped garlic, balsamic vinegar, red pepper flakes, and chopped walnuts. Season with salt and freshly ground black pepper to taste.
Finish and serve: Drizzle the olive oil over the pasta and gently toss once more. Serve immediately with additional crumbled feta and freshly ground black pepper, if desired.