In a small bowl, whisk together the peanut butter, soy sauce, lime juice, broth, sugar, and coconut milk. Cut the chicken into 1-inch-wide strips. Heat the oil in a large skillet over medium-high heat. Add the chicken, chili, ginger, and garlic. Cook, stirring occasionally, until the chicken is golden, about 5 minutes. Add the snow peas and broccoli and cook until the vegetables are just tender, about 1 minute. Add the peanut sauce and cook until the mixture has thickened slightly and the chicken has cooked through, about 3 minutes. Garnish with the cilantro. Serve over cooked rice, if desired.
Tip: You can easily substitute beef or shrimp for the chicken in this recipe. For beef, follow the same directions. For shrimp, cook all the vegetables, then add the shrimp, cook for 1 minute or until pink, add the peanut sauce, and finish the recipe from there.