Bring coconut milk, 1 1/2 cups chicken broth, water, butter, and sugar to a boil in a large saucepan. Stir in rice. Return to a boil; reduce heat and simmer until liquid has been absorbed and rice is fluffy, about 25 minutes. Remove from heat and let sit for an additional 5 minutes. Remove lid and fluff with a fork. Let cool in the refrigerator at least 2 hours.
Whisk together soy sauce, hoisin sauce, 2 tablespoons chicken broth, 1 1/2 tablespoons chili oil, and sesame oil in a small bowl. Set sauce mixture aside.
Spray a large non-stick skillet with cooking spray and set over medium heat. Pour in eggs; scramble to desired doneness, 3 to 4 minutes. Transfer to a bowl and set aside.
Heat olive oil and remaining 1/2 tablespoon chili oil in the same non-stick skillet over medium heat. Add onion, bell pepper, and garlic; cook and stir until softened, about 3 minutes.
Return scrambled eggs to the skillet and add cooked shrimp, peas, and green onions. Cook and stir over medium heat until peas are tender, about 3 minutes. Add cooked and cooled rice; cook and stir until rice is heated through, about 5 minutes. Pour in sauce mixture and toss to coat. Let sit, covered, on low heat to allow rice to absorb sauce flavor, about 10 minutes.