In a large pot of boiling salted water, cook pasta according to package instructions. Within the last 2 minutes of cooking time, add broccoli; drain well.
Heat olive oil in a large skillet over medium high heat. Season chicken breasts with salt and pepper, to taste. Add to skillet and cook, flipping once, until cooked through, about 3-4 minutes per side. Let cool before dicing into bite-size pieces.
Heat a large skillet over medium high heat. Stir in milk, flour, garlic and Dijon, until smooth and slightly thickened, about 2-3 minutes; season with salt and pepper, to taste.
Stir in pasta, broccoli, chicken, sun dried tomatoes and cheeses until well combined, about 2-3 minutes.