In a medium bowl, whisk together mayonnaise, tomato paste, 1 tbsp melted butter, garlic powder, paprika, sugar, and water until completely smooth. Cover and refrigerate for at least 30 minutes.
Heat a large wok or skillet over medium-high heat. Melt 1 tbsp of butter and add the diced chicken. Cook for 5-7 minutes until fully cooked and browned. Remove from the pan and set aside.
In the same wok, scramble the eggs until just cooked, then remove and set aside with the chicken.
Melt the remaining 1 tbsp of butter in the wok. Add the frozen peas and carrots, cooking for 2 minutes until thawed.
Add the cold cooked rice to the wok, pressing down with a spatula to break up any clumps. Stir-fry for 3-4 minutes.
Add the cooked chicken and scrambled eggs back to the pan. Drizzle with soy sauce and sesame oil. Toss well to combine and cook for another 2 minutes until heated through.
Remove from heat, stir in the green onions, and serve immediately with the chilled creamy sauce.