In a small pot, combine the rice, a big pinch of salt, and 1 cup of water. Heat to boiling on high. Once boiling, reduce the heat to low. Cover and cook, without stirring, 12 to 14 minutes, or until the water has been absorbed and the rice is tender. Turn off the heat and fluff with a fork.

While the rice cooks, wash and dry the fresh produce. Cut the mushrooms into bite-sized pieces. Thinly slice the scallions, separating the white bottoms and hollow green tops. Cut off and discard the stems of the peppers; remove the cores, then thinly slice lengthwise. Place in a bowl; add the sliced white bottoms of the scallions. Halve the fresh tomatoes. 

While the rice continues to cook, in a medium pan (nonstick, if you have one), heat half the sesame oil on medium-high until hot. Add the mushroom pieces in an even layer. Cook without stirring, 3 to 4 minutes, or until browned. Add the sliced peppers and white bottoms of the scallions; season with salt and pepper. Cook, stirring occasionally, 1 to 2 minutes, or until slightly softened. Add the halved fresh tomatoes; season with salt and pepper. Cook, stirring occasionally, 30 seconds to 1 minute, or until combined. 

To the pan, add the canned tomatoes (carefully, as the liquid may splatter), demi-glace, and as much of the gochujang as you’d like, depending on how spicy you’d like the dish to be; season with salt and pepper. Cook, stirring occasionally, 3 to 4 minutes, or until combined. Using a spoon, create two shallow wells in the center of the cooked vegetables and sauce. Crack an egg into each well; season with salt and pepper. Cover the pan with foil and cook 4 to 6 minutes, or until the egg whites are set and the yolks are cooked to your desired degree of doneness. Turn off the heat. 

While the eggs cook, to the pot of cooked rice, add the sesame seeds and remaining sesame oil. Stir to combine. Serve the finished rice topped with the cooked eggs, vegetables, and sauce. Garnish with the sliced green tops of the scallions. Enjoy!