Wash eggplant and zucchini. Quarter them and remove seeds. Cut the remaining flesh into bite-sized pieces.
Cut chicken into bite-sized cubes. In a bowl, mix with ginger, salt, and pepper. Refrigerate for 5 minutes.
Peel and finely chop onion and garlic. Core and finely chop large chilli peppers. Finely chop small chilli peppers (with seeds). Heat olive oil in a large pan over medium-high heat. Sauté onion, garlic, and chilli peppers for 2-3 minutes. Add chicken and cook for 8-10 minutes, stirring occasionally, until cooked through (74 °C / 165 °F internal temperature).
Add eggplant and zucchini to the pan. Cook for 5-7 minutes, stirring occasionally, until tender-crisp.
In a small bowl, stir together tomato paste, some water, and cooking cream. Pour into the pan and stir well. Simmer for 2-3 minutes. Season with salt and pepper.
Alternatively, cook this dish in a wok using the same method.