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Step 1
Melt butter in a large skillet over medium-high heat. Saute carrots and onion for about 4 minutes. Add garlic during the last few seconds so that it becomes fragrant but does not burn.
Step 2
Combine broccoli and chicken broth in a microwave-safe bowl. Steam in the microwave until tender, about 3 minutes. Drain off chicken broth. Coarsely chop the florets and add to the carrot mixture. Stir to combine and set aside.
Step 3
Remove skin from the rotisserie chicken. Using a sharp knife, carefully separate pieces. Cut meat into small cubes, making sure to pick through and discard any bones.
Step 4
Combine butter and flour in a heavy saucepan over medium heat. Stir to form a paste. Slowly pour in milk. Cook, whisking constantly, until sauce thickens, about 7 minutes. Stir in white Cheddar cheese and garlic salt.
Step 5
Preheat the oven to 350 degrees F (175 degrees C).
Step 6
Set aside 1/2 cup Cheddar cheese for the topping. Spread about 1/2 cup of the sauce over the bottom of an 8x8-inch casserole dish. Add a layer of lasagna noodles, broccoli mixture, cheese, and chicken. Repeat layers, ending with sauce. Sprinkle reserved Cheddar cheese and panko bread crumbs over the top.
Step 7
Cover lasagna with foil and bake in the preheated oven for 35 minutes. Uncover and bake for 5 minutes more. Allow to rest for 7 minutes before serving.