Combine meat, brown sugar, and soy sauce in a bowl
Combine gochujang, water, and sesame oil in a small bowl.
Cook rice according to package or rice cooker directions
Turn oven to its lowest setting. You will use this to keep vegetables warm as you cook them.While rice is cooking, cut onion into thin slices. Add oil to a pan set on a medium-hot burner, and saute onions, turning regularly. Cook until they are just translucent, but still have a bit of crunch. Put them in a pile on a baking sheet and place sheet in the warm oven. Peel carrots and slice them thin, add more oil, and cook as you did the onions. If you're reasonably fast and a good multi tasker, you can do this while doing the last step. So you'll be peeling and slicing the carrots while the onion is cooking, and you can start cooking the carrots as soon as the pan is free. When the carrots are done place them on the sheet beside the onion.
Add another splash of oil and the sesame seeds. When they just start to brown add the spinach, and cook, then put spinach in the oven with the other veggies.
Cook the meat in a single layer. Depending on the size of your pan you may want to do this in two batches. Brown thoroughly, but don't overcook.
Start frying some eggs. While they're cooking, assemble bowls with rice, veggies, and meat. Top each with an egg and gochujang sauce.