Preheat oven to 350˚F.
Fill a large pot with water and bring to a simmer. Add the chicken breasts and gently poach for 10 minutes or until the chicken breasts are cooked through. Cooking time will vary depending on the size of the chicken breasts. Transfer the cooked breasts to a paper towel-lined plate. Dice the chicken into 1/2-inch cubes.
While the chicken is poaching, heat the butter in a large skillet. Fry the onion and garlic until fragrant and translucent, about 5 minutes. Add the heavy cream and turn the heat to low.
In the same pot of water, simmer the broccoli for five minutes. Using a slotted spoon, transfer to the cream sauce in the skillet. Add the diced chicken, salt and pepper.
In the same pot as the broccoli, cook the pasta according to package instructions. Once cooked, transfer to the skillet using the slotted spoon. Add 1 cup of the parmesan cheese and the ricotta and gently toss/stir to evenly combine all ingredients. If you find the mixture to be dry, add some of the pasta cooking liquid. Transfer to an oven-proof baking dish (9 x 13 works well). Top with the remaining 1/2 cup parmesan cheese and bake in the oven for about 15 minutes until bubbling and warmed through.