In a large pot of salted boiling water, cook the linguine according to package directions until al dente. Reserve a ½ cup of pasta water, then drain pasta and set aside.

Meanwhile, in a large skillet over medium heat, heat oil. Add garlic and cook until fragrant, 1 minute. Sprinkle flour over evenly, then stir and cook until mixture is lightly golden.

While whisking, gradually add broth, 2 tablespoons at a time, waiting for mixture to become completely smooth before adding more broth. Bring mixture to a boil, then slowly add in milk while whisking. Bring to a simmer and cook until sauce is thickened, 2 to 3 minutes.

Remove from heat and add Parmesan and yogurt. Season with salt, pepper, and a pinch of red pepper flakes.

Add pasta and a 1/4 cup reserved pasta water to sauce and toss to combine. If sauce is too thick add more pasta water, a tablespoon at a time, until desired consistency.

Garnish with parsley before serving.