In a large skillet, heat the 2 tablespoons of sesame oil over medium-high heat. Allow the oil to shimmer, which indicates it's hot and ready for cooking.
Add the 2 pounds of cubed chicken breast to the skillet. Sauté until the chicken is golden brown and cooked through, about 5-7 minutes. Stir occasionally to ensure even cooking.
Once the chicken is cooked, reduce the heat to medium and add 2 tablespoons of curry powder, 3-4 tablespoons of red curry paste, and 1 tablespoon of tomato paste. Stir well to coat the chicken in the spices.
Next, add 2 tablespoons of salted butter, 2 chopped garlic cloves, and 1 tablespoon of chopped fresh ginger. Stir until the butter melts and the garlic and ginger become fragrant, about 1-2 minutes.
Toss in the 2 cups of chopped broccoli florets. Stir to combine and let them cook for about 2 minutes until they begin to soften.
Slowly add the 2 1/2 cups of canned coconut milk to the skillet. Stir until all ingredients are well combined and the mixture is creamy. Allow it to simmer for about 10 minutes, letting the flavors meld together.
Once the curry has thickened slightly, remove it from the heat. Stir in the 1/2 cup of fresh chopped cilantro for a burst of freshness. Taste and adjust seasoning if necessary.
