Prepare the marinade by whisking together soy sauce, brown sugar, sesame oil, gochujang, minced garlic, grated ginger, black pepper, and red pepper flakes in a bowl.
Marinate the flank steak in the mixture for at least 30 minutes or up to 4 hours in a refrigerator.
Create quick pickled cucumbers by mixing rice vinegar with sugar and salt; add thin cucumber slices and let sit for 15 minutes.
For spicy mayo, combine mayonnaise with gochujang, sesame oil, and rice vinegar until smooth.
Grill or skillet-cook the marinated steak over medium-high heat for about 3-5 minutes per side until cooked to desired doneness; let rest before slicing.
Assemble bowls with cooked rice topped with sliced steak, pickled cucumbers, and generous drizzles of spicy mayo.