Preheat oven to 375˚F.
Pour chicken and peas into a large mixing bowl and toss together.
Place 1 ½ tablespoons butter in a large skillet and place over medium-high heat. Add mushrooms and saute for 2 to 3 minutes. Season with salt and pepper and add to the chicken and peas.
Add remaining butter to the skillet and add garlic and onions and sauté for 2 to 3 minutes.
Pour cream into the mixture and lower the heat to medium-low and simmer. Season with salt and pepper and continue to simmer until the cream reduces by ½ cup, 6 to 7 minutes.
Once the cream has reduced begin whisking in Parmesan, ½ ounce at a time, until all about 6 ounces of Parmesan has been added and the sauce is smooth.
Season with salt and pepper and continue to simmer the sauce until it thickens enough to coat the back of a wooden spoon, 4 to 6 minutes.
Reserve 2 cups of the alfredo sauce and pour the remaining sauce over the chicken and pea mixture and fold together. Adjust seasonings.
To assemble: Pour 1 cup alfredo sauce into the bottom of an 8”x8” baking dish and set aside. Pace a cooked lasagna sheet onto a clean surface and top with a layer of the creamy chicken mixture.
Tightly roll the lasagna sheet up completely. Carefully place it into the prepared baking dish, spiral side-up. Repeat until all of the sheets and filling have been used and snuggly fit into the baking dish. Drizzle roll ups with remaining alfredo sauce.
Sprinkle the top of the dish with the half of the remaining Parmesan and place baking dish in the oven for about 25 minutes. Remove from oven, top with remaining Parmesan and allow the dish to cool slightly. Serve.