Prepare the Spiral-cut Mini Cucumbers: Spiral-cut the mini cucumbers.
Make the Sauce: In a small bowl, mix together minced garlic, red chili peppers, sesame seeds, soy sauce, rice wine vinegar, brown sugar, and sesame oil.
Combine Cucumbers and Sauce: In a large bowl, toss the spiral-cut cucumbers with the prepared sauce until the cucumbers are well-coated.
Serve Over Warm White Rice: Divide the warm, cooked white rice among serving plates. Top the rice with the spiral-cut cucumbers and drizzle any remaining sauce over the dish.
Garnish (Optional): Garnish with additional sesame seeds or sliced green onions for added flavor and presentation.