3 oz. light or regular cream cheese, diced into cubes
1/2 cup (1.5 oz) finely shredded parmesan, plus more for serving
3 Tbsp heavy cream
1 Tbsp lemon zest, plus more for serving
1 Tbsp fresh lemon juice
Prepare pasta in salted water according to directions listed on package, adding in broccoli during last 5 minutes of boiling pasta (so they will both boil together during last 5 minutes, then drain them together. Reserve 1/4 cup pasta water just in case you want to thin sauce, I didn't use it but I always save some just in case).
In a large and deep skillet or pot, melt butter over medium heat then add in garlic and flour and cook 1 minute, stirring constantly. While whisking slowly pour milk into flour mixture, then cook, whisking vigorously to smooth lumps until mixture begins to thicken. Add in cream cheese and parmesan and whisk until melted (it will look lumpy at first but will begin to smooth). Mix in cream and season with salt and pepper to taste (I liked this with a fair amount of pepper). Stir in lemon zest and lemon juice.
Toss drained pasta and broccoli into sauce mixture along with chicken (thin with reserved pasta water if needed). Serve warm topped with additional parmesan, lemon zest and pepper as desired.