Making the sauce: Mix all sauce ingredients together in a small bowl or glass.
Making the fried rice: In an oiled large wok or deep skillet over medium-high heat, fry the cooked rice. Separate the grains to fluff and ensure all of the rice cooks evenly -- you don't want lumps. Stir constantly, keep everything moving. After about 2 or 3 minutes, pour over 2 tbsp of soy sauce. Mix it in well and continue to fry.
My husband likes his egg to coat most of the rice, I prefer big chunks of egg. For his way, pour the beaten egg over the rice and stir it in well, continuing to stir constantly so that all of the egg cooks up nicely. For my way, push the rice to the sides, leaving a largish circle of pan in the center. Pour the eggs into the cleared center and scramble. Once the eggs are mostly cooked, stir into the rice.
When the rice is nicely browned, add the green onions and fry for another 30 seconds. Remove to a bowl and keep warm.
Making the stirfry: In a large skillet or wok, lightly oiled and set over medium-high heat, begin by frying up the onions until nicely browned and soft. Remove to the bowl.
Next, add squash, broccoli and carrot. Add a bit of water and cover for 2 minutes to steam them a bit before frying. Remove cover and add garlic and mushrooms. Fry all together for a couple of minutes until the mushrooms soften. Add sauce. Continue to fry, stirring frequently for another 2 minutes. Add peas, cook for 1 minute, then add green onions. Stir in the onions. Taste a bit of broccoli, make sure it's cooked al dente.
Serve over fried rice.