Preheat your oven to 375°F.
Boil the lasagna noodles. Bring a large pot of water to a boil over high heat. Add the dry noodles and cook according to package instructions, just until al dente. Drain the noodles and rinse them with cold water.
Poach the chicken breast. While the noodles are boiling, place the raw chicken breast in the bottom of a medium-sized saucepan. Cover the chicken with cold water, filling the saucepan to within one inch from the top. Bring the water to a gentle boil over high heat, then reduce the heat to a simmer and cook the chicken for about 15 minutes, or until cooked through.
Shred the cooked chicken. When the chicken has reached an internal temperature of at least 165°F, transfer the chicken to a large mixing bowl. Shred the chicken using two forks or an electric mixer.
Make the alfredo sauce. Melt the butter in the bottom of a medium-sized saucepan over low heat. Add the flour and whisk the butter and flour for about 30 seconds, until a smooth paste forms. Pour the milk in, increase the heat to medium, and stir continuously until the milk thickens. This should only take about 5 minutes. You'll know the milk has thickened when it starts to coat the sides of the saucepan. Add the parmesan cheese, garlic powder, dried oregano, salt, and pepper to the mixture. Whisk until smooth, then remove from the heat.
Assemble the lasagna. Spread ½ cup of alfredo sauce evenly on the bottom of a 9" x 13" casserole dish. Layer 3 cooked lasagna noodles onto the sauce. Sprinkle 1 cup of shredded chicken onto the noodles. Sprinkle 1 cup of chopped broccoli onto the chicken. Layer the sauce, noodles, chicken, and broccoli onto the lasagna two more times. Add a final layer of lasagna noodles to the top of the dish. Cover the noodles with the remaining alfredo sauce and 2 cups of shredded mozzarella cheese.
Bake the lasagna. Cover the lasagna with foil and bake at 375°F for 25 minutes. Uncover and continue baking for 5 more minutes, or until the cheese is melted and bubbly. Remove the cooked lasagna from the oven, let it rest for 10 minutes, then serve and enjoy!