Make the marinated eggs

1. Bring a large pot of water to a boil over high. Add eggs, and cook 6 minutes and 30 seconds. Meanwhile, fill a large bowl with ice and water. Transfer eggs to ice bath, and let stand until cooled, about 10 minutes. Stir together soy sauce, 1/3 cup water, honey, scallions, garlic, sesame seeds, and crushed red pepper in a medium bowl. Peel eggs, and submerge in marinade. Cover and refrigerate at least 1 hour or up to 12 hours. Remove eggs and discard marinade.

Make the rice bowl

1. Rinse rice in a strainer under cold water, stirring with your fingers until water runs clear. Transfer rice to a small saucepan; add 1 1/2 cups water and salt, and bring to a boil over medium, stirring once. Reduce heat to low. Cover and cook, undisturbed, 15 minutes. Remove from heat; let stand, covered, 5 minutes. Uncover and fluff rice with a fork.

2. Stir together cucumber, togarashi, and sesame oil in a medium bowl; set aside. Heat olive oil in a medium-size nonstick skillet over medium. Add garlic and crushed red pepper; cook, stirring often, until fragrant, about 30 seconds. Add spinach and soy sauce; cook, stirring often, until spinach is just wilted, about 1 minute and 30 seconds. Remove from heat.

3. Slice marinated eggs in half lengthwise. Divide rice among four serving bowls, and top with eggs, cucumber, spinach, and kimchi. Garnish with scallions and additional togarashi.