In large bowl, whisk red pepper paste, sesame oil, soy sauce, sugar, garlic and 1/4 cup of water until smooth; set aside 1/2 cup of sauce. To bowl with remaining sauce, add beef and pinch salt, tossing to coat. Let stand at least 10 minutes or refrigerate up to overnight.
Add beef to pressure-cooker pot along with mushrooms. Cover, lock and bring up to pressure on high. Reduce heat to medium-low, maintaining pressure. Cook 10 minutes.
While beef cooks, toss cucumber with vinegar and 1/4 teaspoon of salt; set aside.
Release pressure by using quick-release function. Divide spinach among 6 serving bowls; top each with 1 cup of rice. Drain cucumbers. Top rice with beef, mushrooms, cucumbers, green onions, carrots, kimchi and sesame seeds; drizzle with reserved sauce.