Prepare the white sauce by melting the butter in a saucepan over medium high heat then add in the garlic and flour.
Whisk to combine and continue stirring for 3-5 minutes.
Slowly add in the milk and chicken stock in ½ cup increments. Stirring in between and allow the mixture to thicken up between each addition.
Once all of the liquid has been added stir in the salt, pepper, parmesan cheese, broccoli, and pesto. Cook for 5-7 minutes then remove from heat.
Preheat the oven to 350 degrees.
In a 9x13 baking dish add ½ cup of the sauce and spread it to cover the bottom of the dish.
Add one layer of lasagna noodles and top with another cup of the white sauce.
Top with ½ of the ricotta cheese, ⅓ of the chicken, ⅓ of the shredded mozzarella, and then another layer of lasagna noodles.
Top the lasagna noodles with more sauce and continue layering until all ingredients are gone.
Finish the lasagna on top with an extra sprinkle of mozzarella cheese and bake for 15 minutes uncovered.
Cover the lasagna with foil and bake another 20-25 minutes.