Step 1: Preheat the Oven - Set your oven to 400 degrees and grease a large sheet pan. I like to do this first because once the chopping starts, everything moves pretty quickly. A hot oven helps the chicken cook through while giving the vegetables a little roasted flavor around the edges. Use the biggest sheet pan you have so the ingredients can spread out instead of steaming in a pile.
Step 2: Chop the Vegetables - Chop the broccoli into small florets, dice the red bell pepper, and cut the carrots into 1 inch pieces before halving them. This part matters more than folks think. If the carrots are too thick, they will still be too firm when the chicken is done. If the broccoli is too large, the tops may brown before the stems are tender. Keep everything bite sized and fairly even, and dinner will treat you right.
Step 3: Cut the Chicken - Dice the boneless skinless chicken breast into bite sized pieces. Try to keep the pieces close in size so they all cook at the same pace. This is one of those little dad lessons that saves trouble later. Big chunks and tiny chunks on the same pan mean some pieces get dry while others are still catching up. A steady size keeps the chicken juicy and dependable.
Step 4: Coat the Chicken - In a large bowl, mix the sesame oil, cornstarch, salt, garlic powder, and paprika. Add the chicken pieces and stir until every piece is coated. The mixture may look simple, but it does important work. The sesame oil adds flavor, the seasonings build the base, and the cornstarch helps the chicken bake with a light coating instead of drying out. Use a silicone spatula or clean hands and make sure there are no plain pieces hiding at the bottom of the bowl.
Step 5: Arrange the Chicken on the Pan - Spread the coated chicken across the greased sheet pan. Give the pieces a bit of space where you can. They do not need their own little apartments, but they should not be stacked on top of each other either. When the chicken has room, it cooks more evenly and gets better texture. If everything is crowded, it can steam, and we are looking for tender chicken with those nice roasted edges.
Step 6: Add the Vegetables and Cashews - Add the broccoli, red bell pepper, carrots, and sliced water chestnuts to the sheet pan around the chicken. Sprinkle the cashews over the top. I like seeing all those colors on the pan at this point because it already looks like dinner is headed somewhere good. The cashews toast a bit as they bake, the vegetables soften, and the chicken starts cooking before the sauce goes on.
Step 7: Bake the First Round - Transfer the sheet pan to the oven and bake for 10 minutes. This first bake gives the chicken a head start and lets the vegetables begin to roast before the sauce is added. If you add the sauce too early, the sugars can darken too fast and the pan can get a little too sticky. Ten minutes lets everything firm up just enough so the sauce can coat it nicely in the next step.
Step 8: Whisk the Sauce - While the pan is in the oven, whisk together the brown sugar, honey, soy sauce, and minced garlic in a small bowl. The sauce should look glossy and smell sweet, salty, and garlicky. Give it a good whisk so the brown sugar starts to dissolve. This sauce is the heart of the recipe, and it brings all the chicken, vegetables, and cashews together in that cozy cashew chicken way.
Step 9: Sauce and Toss - Remove the sheet pan from the oven and pour the sauce over everything. Toss gently to coat the chicken, vegetables, water chestnuts, and cashews. Be careful here because the pan is hot, and nobody needs a heroic dinner injury. Use a silicone spatula to turn everything over just enough so the sauce touches every bite. It may not look thick yet, but it will tighten up a bit as it finishes baking.
Step 10: Finish Baking - Return the sheet pan to the oven and bake for another 5 to 10 minutes, until the chicken is cooked through and the vegetables are tender. The chicken should reach 165 degrees in the center if you are using a meat thermometer. The sauce will bubble around the edges and cling to the chicken. Once it is done, sprinkle diced green onions over the top and serve it while everything is hot and glossy.