Preheat oven to 425 degrees. Spray a 3-qt rectangle baking dish with non-stick cooking spray and set aside.Next, in a mixing bowl whisk together Gochujang, soy sauce, toasted sesame oil, honey, and rice vinegar. Set aside.In a large Dutch oven preheated to medium-high heat add 1 tbsp olive oil to the skillet. Add the ground pork and break up using a wooden spoon. Cook the pork until no longer pink about five minutes. Remove the pork from the Dutch oven using a slotted spoon and set aside on a plate.In the same skillet add the remaining 1 tbsp olive oil. Add the mushrooms, onion and garlic. Cook for a few minutes until the mushrooms have browned.Next, add in the kale and carrots. Cook for additional two minutes. Add the rice, reserved ground pork, and stir in the Gochujang mixture. Toss to make sure everything is combined.Spoon the entire mixture into the prepared baking dish. Spread everything into an even layer. Next, make 6 indents in the mixture with a back of a spoon. Crack an egg into each indent. Place the baking dish into the oven and cook for about 20 minutes or until the eggs are set.Remove from oven and garnish with green onions and Sriracha.