In a large pot of salted boiling water, cook bowties according to package directions until al dente. During the last 2 minutes of cooking, add broccoli and cook until bright green. Drain and return to pot.
Meanwhile, in a large skillet over medium-high heat, heat oil. Add chicken breasts and season with salt and pepper. Cook until golden, 8 minutes per side. Transfer to a plate to let rest, then thinly slice.
Add milk, Parmesan, cream cheese, and garlic to skillet and let melt and thicken, stirring occasionally. Season with salt and pepper.
Add cooked bowties and broccoli and chicken to skillet and toss until completely combined.