Prepare the ingredients: Slice the bagel in half. Crack eggs into a bowl and whisk until smooth. Season with salt and black pepper. Set aside.
Toast the bagel: Toast the bagel halves in a toaster or on a grill pan until golden brown. Spread vegetable cream cheese on each half. Set aside on serving plates.
Heat the skillet: Preheat a non-stick skillet over medium-low heat. Add half the chili oil and red pepper flakes. Swirl to coat.
Cook the eggs: Add butter to the skillet. Once melted, pour in the eggs. Gently scramble using a spatula until just set, about 1–2 minutes. Remove from heat.
Finish and serve: Divide the scrambled eggs between two plates. Drizzle the remaining chili oil over the eggs. Serve with the toasted bagel halves and glasses of cold orange juice.