Preheat the oven to 350 degrees F.
Heat olive and sesame oil in small saucepan with tight fitting lid over low heat for 1-2 minutes. Add rice and stir occasionally, lightly frying the rice for about 10-15 minutes. Add the peas and carrots and stir for 2 minutes. Add the chicken stock/broth, water and about 1/4 teaspoon salt. Bring to a boil, cover with the lid and place in the oven. Bake for about 20 minutes.
Meanwhile, add a little more olive oil to a small frying pan. Add the mushroom pieces with a little salt and pepper. Fry over medium heat until the mushrooms are cooked down and browned, about 5 minutes. Add the broccoli and cook for about another 5 minutes, stirring often. Then add the water chestnuts and green onions to the frying pan. Cook for 2-3 more minutes. Remove from the frying pan and set aside.
Scramble the eggs in a bowl. Add a little olive oil to the frying pan you just cooked the veggies in. Add the eggs and let cook, stirring often until cooked through and scrambled. Add to the veggies and set aside.
Whisk together the coconut aminos (or gluten free soy sauce), rice vinegar, dry mustard and agave in a measuring cup.
Carefully, pull the saucepan out of the oven (make sure not to burn your hands on the handle or lid). Stir the rice, carrot and peas with a fork. Add the liquid aminos mixture and the fried veggie/eggs and stir into the rice. Cover and place back into the oven for another 10 minutes. You want to the rice to absorb the liquid and dry up a little more but not dry out.
Serve fresh out of the oven. Add a little hot sauce to take it to the next level, too.