Bring a large pot of salted water to a boil. Cook the lentil or chickpea pasta according to package directions until al dente. Reserve 1/2 cup of the pasta water, then drain and set aside.
While pasta cooks, season chicken pieces with salt, pepper, and Italian seasoning. Heat olive oil in a large skillet over medium-high heat. Add chicken and cook until golden and cooked through (internal temperature 165°F/74°C), about 5-7 minutes. Remove from skillet and set aside.
In the same skillet, reduce heat to medium. Add garlic and sun-dried tomatoes, sautéing for 1 minute until fragrant. Pour in chicken broth and scrape up any browned bits. Let it simmer for 2 minutes.
Remove the skillet from heat. Slowly whisk a few spoonfuls of the hot broth into the room-temperature Greek yogurt to warm it gently. Then, stir the yogurt mixture back into the skillet. This prevents curdling.
Return the skillet to low heat. Stir in Parmesan until melted. Add spinach and cook until wilted, about 2 minutes. Return the cooked chicken and drained pasta to the skillet. Toss everything together, adding reserved pasta water a splash at a time until the sauce coats the pasta nicely. Adjust seasoning with salt, pepper, and red pepper flakes.
Divide among bowls, top with fresh basil and extra Parmesan. Serve immediately.