Preheat oven to 425°F. Place a sheet pan in the oven while it is heating. In a small bowl, whisk the sauce ingredients. Set aside.
Toss the broccoli with the olive oil, garlic, red pepper flakes, lemon zest, salt, and pepper. Set aside.
Next, layer 1 slice of ham and 2 halved slices of Swiss cheese diagonally on top of each thinly-sliced chicken breast. Starting at the end towards you, roll tightly, tucking the ham and cheese into the chicken to prevent it from peeking out too much. Once you get to the end, use one or two toothpicks to secure. Season the chicken with salt and pepper.
Once the oven is heated, grease the sheet pan with cooking spray or neutral oil. Spread the broccoli into an even layer over 3/4 of the sheet pan. Place the chicken rolled side up on the other side. Bake for about 20 minutes, or until the chicken reaches 160°F.
Once the chicken reaches 160°F, turn the broiler onto high. Toss the broccoli, and flip the chicken breasts so they are rolled side down. Brush the sauce over the tops and sides of the chicken and broil for 2-3 minutes until the sauce is thickened, the chicken is browned, and the internal temperature is 165°F. (If the broccoli starts to brown too much, remove it from the pan).
Squeeze the lemon over the broccoli and slice each chicken breast into 2-3 pieces. Enjoy!