Stir cucumber pieces with 1/4 cup gochujang paste in a bowl. Set aside.
Bring about 2 cups of water to a boil in a large pan and stir in spinach; cook until spinach is bright green and wilted. Cook for 2 to 3 minutes. Drain spinach and squeeze out as much moisture as possible; set spinach aside in a bowl and stir soy sauce into spinach.
Heat 1 teaspoon Baguio Canola Oil in large pan and cook and stir carrots until softened. Stir in garlic and cook just until fragrant. Stir in cucumber pieces with gochujang paste. Sprinkle with red pepper flakes, and set the mixture aside in a bowl.
In a large pan, heat 1 tablespoon Baguio Canola Oil and add the beef. Cook for 5minutes per side. In a separate pan, heat 1 teaspoon Baguio Canola Oil and fry the eggs just on one side until yolks are runny but whites are firm.
To assemble the dish, divide cooked rice into 4 large serving bowls; top with spinach mixture, a few pieces of beef, and cucumber mixture. Place 1 egg atop each serving. Drizzle each bowl with 1 teaspoon of sesame oil, a sprinkle of sesame seeds, and a small amount of gochujang paste if desired.