Spray a large slow cooker with nonstick cooking spray. Place the cream cheese, onions, and garlic in a microwave-safe bowl with 1 teaspoon salt, and 1/4 teaspoon ground pepper. Microwave on high for 1-2 minutes, until the cream cheese is molten and the onions are soft. Pour in the milk and whisk until smooth.
Cut the broccoli into small florets and slice the chicken into small bite-size pieces.
Spread a small amount of the cream cheese sauce in the bottom of the slow cooker. Then cover it with a single layer of dried lasagna sheets. Break the noodles to fit into the slow cooker along the round edges. Sprinkle the pasta sheets with 1 cup of broccoli, one-quarter of the chopped chicken, and 1 cup of shredded cheese. Drizzle one-quarter of the remaining cream cheese sauce over the ingredients. Repeat the lasagna sheet, chicken, broccoli, cheese, and sauce layering until you have 4 full layers.
Place the crock in the slow cooker and cover with the lid. Slow cooker for 2-3 hours on high, or 4-6 hours on low. Cut and serve warm.