Preheat the oven to 375°F.
Grease a 9x13-inch casserole dish with nonstick cooking spray or a suitable cooking grease.
To prepare the broccoli pesto, add the broccoli florets, basil leaves, extra-virgin olive oil, garlic cloves, salt, pepper, and grated Parmesan cheese to a food processor.
Pulse until the ingredients are combined and the mixture reaches a pesto-like consistency.
Taste the pesto and adjust the salt and pepper as needed.
Set the broccoli pesto aside.
To prepare the Alfredo white sauce, melt the unsalted butter in a medium saucepan over medium heat.
Add the minced garlic and cook for 30 to 60 seconds, or until fragrant.
Whisk in the flour.
Cook the flour mixture for 1 minute, stirring continuously, until lightly golden.
Slowly pour in the milk while whisking constantly to help prevent lumps.
Add the chicken broth or vegetable broth.
Add the ricotta cheese.
Whisk until the sauce is smooth and creamy.
Stir in the dried basil.
Season with salt and pepper to taste.
Reduce the heat to medium-low.
Simmer the sauce for 5 to 8 minutes, stirring often, until thickened.
Remove the sauce from the heat.
Taste and adjust the seasoning as needed.
Spread a thin layer of the prepared Alfredo white sauce over the bottom of the greased casserole dish.
Place 3 no-boil lasagna noodles over the sauce.
Spread additional Alfredo white sauce over the noodles.
Add several spoonfuls of broccoli pesto over the sauce.
Add an even layer of shredded chicken.
Sprinkle with grated Parmesan cheese.
Add a layer of shredded mozzarella cheese.
Repeat the layering process 2 more times with noodles, Alfredo white sauce, broccoli pesto, shredded chicken, Parmesan, and mozzarella.
Finish with a final layer of noodles, Alfredo white sauce, and mozzarella cheese.
Ensure the top layer of noodles is completely covered with sauce and cheese to allow the noodles to soften properly during baking.
Bake the lasagna uncovered for 30 minutes.
Carefully cover the baking dish with foil.
Continue baking for an additional 10 to 15 minutes, or until the cheese is melted, bubbly, and the noodles are tender.
Remove the lasagna from the oven.
Let the lasagna rest for 5 to 10 minutes before slicing.
Slice and serve warm.