Cook the linguine in a large pot of salted boiling water according to package directions until al dente; drain and keep warm.
Cut the chicken tenderloins into about 2-inch pieces (or slice breast halves into bite-sized pieces).
In a small bowl, whisk together the salt, black pepper, and all-purpose flour.
Toss the chicken pieces in the flour mixture until evenly coated.
Heat oil in a large saucepan or skillet over medium heat. Working in batches if needed, cook the coated chicken until browned on all sides and cooked through; transfer to a plate and set aside.
Add a little more oil to the pan if it looks dry, then add the minced garlic and sauté about 30 seconds until fragrant.
In a mixing bowl, whisk together the milk and cornstarch until smooth.
Slowly pour some of the milk mixture into the hot pan while whisking constantly; allow the sauce to thicken slightly before adding more, repeating until all the milk mixture is incorporated and the sauce is thickened.
Return the cooked chicken to the pan, add the chopped dill and grated Parmesan, and stir to combine and coat the chicken in the sauce.
Cook for 2 to 3 minutes more to warm through and meld flavors.
Add the drained pasta to the sauce and toss until evenly coated.
Let the pasta rest for about 5 minutes, then serve.